https://www.mdu.se/

mdu.sePublications
Change search
Refine search result
1234 1 - 50 of 192
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1. Abramov, V.
    et al.
    Paal, E.Tallinn University of Technology.Silvestrov, Sergei D.Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Stolin, A.Chalmers University of Techology.
    Proceedings of the 3rd Baltic-Nordic Workshop “Algebra, Geometry, and Mathematical Physics”2008Conference proceedings (editor) (Refereed)
  • 2.
    Abramov, Viktor
    et al.
    University of Tartu, Estonia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    3-Hom-Lie Algebras Based on σ-Derivation and Involution2020In: Advances in Applied Clifford Algebras, ISSN 0188-7009, E-ISSN 1661-4909, Vol. 30, no 3, article id 45Article in journal (Refereed)
    Abstract [en]

    We show that, having a Hom-Lie algebra and an element of its dual vector space that satisfies certain conditions, one can construct a ternary totally skew-symmetric bracket and prove that this ternary bracket satisfies the Hom-Filippov-Jacobi identity, i.e. this ternary bracket determines the structure of 3-Hom-Lie algebra on the vector space of a Hom-Lie algebra. Then we apply this construction to two Hom-Lie algebras constructed on an associative, commutative algebra using σ-derivation and involution, and we obtain two 3-Hom-Lie algebras.

  • 3.
    Akbari, Saieed
    et al.
    Sharif Univ Technol, Dept Math Sci, Tehran, Iran.
    Aryapoor, Masood
    Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran.
    Jamaali, M.
    Sharif Univ Technol, Dept Math Sci, Tehran, Iran.
    Chromatic number and clique number of subgraphs of regular graph of matrix algebras2012In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 436, no 7, p. 2419-2424Article in journal (Refereed)
    Abstract [en]

    Let R be a ring and X subset of R be a non-empty set. The regular graph of X, Gamma(X), is defined to be the graph with regular elements of X (non-zero divisors of X) as the set of vertices and two vertices are adjacent if their sum is a zero divisor. There is an interesting question posed in BCC22. For a field F, is the chromatic number of Gamma(GL(n)(F)) finite? In this paper, we show that if G is a soluble sub-group of GL(n)(F), then x (Gamma(G)) < infinity. Also, we show that for every field F, chi (Gamma(M-n(F))) = chi (Gamma(M-n(F(x)))), where x is an indeterminate. Finally, for every algebraically closed field F, we determine the maximum value of the clique number of Gamma(< A >), where < A > denotes the subgroup generated by A is an element of GL(n)(F). (C) 2011 Elsevier Inc. All rights reserved.

  • 4.
    Alekseev, Aleksandr
    et al.
    Independent University of Moscow (IUM), Bolshoy Vlasyevskiy Pereulok 11, Moscow, 119002, Russian Federation.
    Arutyunov, Andronick
    V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Street, Moscow, 117997, Russian Federation.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    On (σ,τ)-Derivations of Group Algebra as Category Characters2023In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, p. 81-99Conference paper (Refereed)
    Abstract [en]

    For the space of (σ,τ)-derivations of the group algebra C[G] of a discrete countable group G, the decomposition theorem for the space of (σ,τ)-derivations, generalising the corresponding theorem on ordinary derivations on group algebras, is established in an algebraic context using groupoids and characters. Several corollaries and examples describing when all (σ,τ)-derivations are inner are obtained. Considered in details are cases of (σ,τ)-nilpotent groups and (σ,τ)-FC groups.

  • 5.
    Ammar, F.
    et al.
    Faculté des Sciences, Université de Sfax, Tunisia .
    Makhlouf, A.
    Université de Haute Alsace, France .
    Silvestrov, S. D.
    Lund University.
    Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras2010In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 43, no 26, p. 265204-Article in journal (Refereed)
    Abstract [en]

    In this paper we construct ternary q-Virasoro-Witt algebras which q-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using su(1, 1) enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary q-Virasoro-Witt algebras constructed in this paper are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield a Hom-Nambu-Lie algebra structure for q-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary q-Virasoro-Witt algebras we construct, carry a structure of the ternary Hom-Nambu-Lie algebra for all values of the involved parameters.

  • 6.
    Andren, Daniel
    et al.
    Umeå University.
    Hellström, Lars
    Umeå University.
    Markström, Klas
    Umeå University.
    Fast multiplication of matrices over a finitely generated semiring2008In: Information Processing Letters, ISSN 0020-0190, E-ISSN 1872-6119, Vol. 107, no 6, p. 230-234Article in journal (Refereed)
  • 7.
    Arfa, Anja
    et al.
    Jouf University, Saudi Arabia; University of Sfax, Tunisia.
    Saadaoui, Nejib
    Université de Gabès, Tunisia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz Algebras2023In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, p. 33-60Conference paper (Refereed)
    Abstract [en]

    Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids and derivations of multiplicative Hom-Leibniz algebras are considered including the detailed study of 2-dimensional Hom-Leibniz algebras.

  • 8.
    Armakan, Abdoreza
    et al.
    Department of Mathematics, College of Sciences, Shiraz University, P.O. Box 71457-44776, Shiraz, Iran.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Color Hom-Lie Algebras, Color Hom-Leibniz Algebras and Color Omni-Hom-Lie Algebras2023In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, p. 61-79Conference paper (Refereed)
    Abstract [en]

    In this paper, the representations of color hom-Lie algebras have been reviewed and the existence of a series of coboundary operators is demonstrated. Moreover, the notion of a color omni-hom-Lie algebra associated to a linear space and an even invertible linear map have been introduced. In addition, characterization method for regular color hom-Lie algebra structures on a linear space is examined and it is shown that the underlying algebraic structure of the color omni-hom-Lie algebra is a color hom-Leibniz a algebra.

  • 9.
    Armakan, Abdoreza
    et al.
    Shahid Bahonar University of Kerman, Kerman, Iran.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Enveloping algebras of certain types of color hom-Lie algebras2020In: Algebraic Structures and Applications: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rancic / [ed] S. Silvestrov, A. Malyarenko, Milica Rancic, Springer Nature, 2020, Vol. 317, p. 257-284Chapter in book (Refereed)
    Abstract [en]

    In this paper the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free hom-associative color algebra on a hom-module is described for a certain type of color hom-Lie algebras and is applied to obtain the universal enveloping algebra of those hom-Lie color algebras. Finally, this construction is applied to obtain the extension of the well-known Poincaré–Birkhoff–Witt theorem for Lie algebras to the enveloping algebra of the certain types of color hom-Lie algebra such that some power of the twisting map is the identity map.

  • 10.
    Armakan, Abdoreza
    et al.
    Shiraz Univ, Coll Sci, Dept Math, Shiraz, Iran..
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Farhangdoost, Mohammad Reza
    Shiraz Univ, Coll Sci, Dept Math, Shiraz, Iran..
    Enveloping algebras of color hom-Lie algebras2019In: Turkish Journal of Mathematics, ISSN 1300-0098, E-ISSN 1303-6149, Vol. 43, no 1, p. 316-339Article in journal (Refereed)
    Abstract [en]

    In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincare- Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.

  • 11.
    Armakan, Abdoreza
    et al.
    Shiraz University, Iran.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Farhangdoost, Mohammad Reza
    Shiraz University, Iran.
    Extensions of hom-Lie color algebras2021In: Georgian Mathematical Journal, ISSN 1072-947X, E-ISSN 1572-9176, Vol. 28, no 1, p. 2019-2033Article in journal (Refereed)
    Abstract [en]

    In this paper, we study (non-Abelian) extensions of a given hom-Lie color algebra and provide a geometrical interpretation of extensions. In particular, we characterize an extension of a hom-Lie color algebra g by another hom-Lie color algebra h and discuss the case where h has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, curvature and the Bianchi identity for possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie color algebras, i.e., we show that in order to have an extendible hom-Lie color algebra, there should exist a trivial member of the third cohomology.

  • 12.
    Arnlind, Joakim
    et al.
    Linköping University, Sweden.
    Kitouni, Abdennour
    Université de Haute-Alsace, Mulhouse, France.
    Makhlouf, Abdenacer
    Université de Haute-Alsace, Mulhouse, France .
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras2014In: Springer Proceedings in Mathematics and Statistics, Berlin, Heidelberg: Springer, 2014, Vol. 85, p. 123-144Conference paper (Refereed)
    Abstract [en]

    The aim of this paper is to compare the structure and the cohomology spaces of Lie algebras and induced 3-Lie algebras

  • 13.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
    Makhlouf, Abdenacer
    Université de Haute Alsace, Lab. de Mathématiques Informatique et Applications, 4, rue des Frères Lumière, F-68093 Mulhouse, France.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication.
    Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 12, p. 123502-Article in journal (Refereed)
    Abstract [en]

    As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]

    Download full text (pdf)
    fulltext
  • 14.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Germany.
    Makhlouf, Abdenacer
    Université de Haute Alsace, France .
    Silvestrov, Sergei
    Lund University, Sweden.
    Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras2010In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 4, p. 043515-11Article in journal (Refereed)
    Abstract [en]

    The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom-Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom-Nambu-Lie algebras obtained using this construction.

  • 15.
    Arnlind, Joakim
    et al.
    Albert Einstein Institute, Golm, Germany.
    Silvestrov, Sergei
    Lund University.
    Affine transformation crossed product type algebras and noncommutative surfaces2009In: Operator structures and dynamical systems: July 21-25 2008, Lorentz Center, Leiden, The Netherlands, satellite conference of the fifth European Congress of Mathematics, Amer. Math. Soc. , 2009, Vol. 503, p. 1-25Chapter in book (Refereed)
  • 16.
    Aryapoor, Masood
    Mathematics Department, Yale University, 10 Hillhouse Avenue, New Haven, CT 06511, USA.
    Non-commutative Henselian rings2009In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 322, p. 2191-2198Article in journal (Refereed)
    Abstract [en]

    Non-commutative Henselian rings are defined and some basicproperties of them are discussed. It is shown that a local ringwhich is complete in the topology defined by its maximal ideal isHenselian provided that it is almost commutative. Some examplesof non-commutative Henselian rings are also given.

  • 17.
    Aryapoor, Masood
    Yale Univ, Dept Math, Dunham Lab 442, 10 Hillhouse Ave, New Haven, CT 06511 USA.
    Self-dual Yang-Mills equations in split signature2010In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 224, no 5, p. 2022-2051Article in journal (Refereed)
    Abstract [en]

    We study the self-dual Yang Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described. 

  • 18.
    Ataguema, H.
    et al.
    Universit́e de Haute Alsace, France .
    Makhlouf, A.
    Universit́e de Haute Alsace, France .
    Silvestrov, S. D.
    Lund University.
    Generalization of n-ary Nambu algebras and beyond2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 8, p. Article number 083501-Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.

  • 19.
    Attari Polsangi, Ahmad Reza
    et al.
    Department of Mathematics, College of Sciences, Shiraz University, P.O. Box 71457-44776, Shiraz, Iran.
    Farhangdoost, Mohammad Reza
    Department of Mathematics, College of Sciences, Shiraz University, P.O. Box 71457-44776, Shiraz, Iran.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Decomposition of Complete Color Hom-Lie Algebras2023In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, p. 101-120Conference paper (Refereed)
    Abstract [en]

    In this paper, we study some equivalent conditions for a color hom-Lie algebra to be a complete color hom-Lie algebra. In particular, we discuss the relationship between decomposition and completness for a color hom-Lie algebra. Moreover, we check some conditions that the set of αs -derivations of a color hom-Lie algebra to be complete and simply complete. Finally, we find some conditions in which the decomposition into hom-ideals of the complete multiplicative color hom-Lie algebras is unique up to order of hom-algebra.

  • 20.
    Bakayoko, I.
    et al.
    Université de N’Zérékoré, Nzerekore, Guinea.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Multiplicative n-hom-lie color algebras2020In: Algebraic Structures and Applications / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rancic, Springer Nature, 2020, Vol. 317, p. 159-187Chapter in book (Refereed)
    Abstract [en]

    The purpose of this paper is to generalize some results on n-Lie algebras and n-Hom-Lie algebras to n-Hom-Lie color algebras. Then we introduce and give some constructions of n-Hom-Lie color algebras.

  • 21.
    Bakayoko, Ibrahima
    et al.
    Univiversite N'Zerekore, Department of Mathematics, N'Zerekore, Guinea.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Hom-left-symmetric color dialgebras, Hom-tridendriform color algebras and Yau's twisting generalizations2021In: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 32, no 5-6, p. 941-958Article in journal (Refereed)
    Abstract [en]

    The goal of this paper is to introduce and give some constructions and study properties of Hom-left-symmetric color dialgebras and Hom-tridendriform color algebras. Next, we study their connection with Hom-associative color algebras, Hom-post-Lie color algebras and Hom-Poisson color dialgebras. Finally, we generalize Yau's twisting to a class of color Hom-algebras and use endomorphisms or elements of centroids to produce other color Hom-algebras from given one.

  • 22.
    Bakayoko, Ibrahima
    et al.
    Département de Mathématiques, Université de N’Zérékoré, BP 50, N’Zérékoré, Guinea.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Hom-Prealternative Superalgebras2023In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, p. 121-145Conference paper (Refereed)
    Abstract [en]

    The purpose of this paper is to introduce Hom-prealternative superalgebras and their bimodules. Some constructions of Hom-prealternative superalgebras and Hom-alternative superalgebras are given, and their connection with Hom-alternative superalgebras are studied. Bimodules over Hom-prealternative superalgebras are introduced, relations between bimodules over Hom-prealternative superalgebras and the bimodules of the corresponding Hom-alternative superalgebras are considered, and construction of bimodules over Hom-prealternative superalgebras by twisting is described.

  • 23.
    Ben Hassine, Abdelkader
    et al.
    Univ Bisha,Dept Math, Sabt Al Alaya, Saudi Arabia.;Univ Sfax, Fac Sci, Sfax, Tunisia..
    Chtioui, Taoufik
    Univ Sfax, Fac Sci, Sfax, Tunisia..
    Mabrouk, Sami
    Univ Gafsa, Fac Sci, Gafsa, Tunisia..
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Structure and cohomology of 3-Lie-Rinehart superalgebras2021In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 49, no 11, p. 4883-4904Article in journal (Refereed)
    Abstract [en]

    We introduce a concept of 3-Lie-Rinehart superalgebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we study the relationships between a Lie-Rinehart superalgebra and its induced 3-Lie-Rinehart superalgebra. The deformations of 3-Lie-Rinehart superalgebra are considered via a cohomology theory.

  • 24.
    Bergander, Philip
    Mälardalen University, School of Education, Culture and Communication.
    Twisted derivations, quasi-hom-Lie algebras and their quasi-deformations2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Quasi-hom-Lie algebras (qhl-algebras) were introduced by Larsson and Silvestrov (2004) as a generalisation of hom-Lie algebras, which are a deformation of Lie algebras. Lie algebras are defined by an operation called bracket, [·,·], and a three-term Jacobi identity. By the theorem from Hartwig, Larsson, and Silvestrov (2003), this bracket and the three-term Jacobi identity are deformed into a new bracket operation, <·,·>, and a six-term Jacobi identity, making it a quasi-hom-Lie algebra.

    Throughout this thesis we deform the Lie algebra sl2(F), where F is a field of characteristic 0. We examine the quasi-deformed relations and six-term Jacobi identities of the following polynomial algebras: F[t], F[t]/(t2), F[t]/(t3), F[t]/(t4), F[t]/(t5), F[t]/(tn), where n is a positive integer ≥2, and F[t]/((t-t0)3). Larsson and Silvestrov (2005) and Larsson, Sigurdsson, and Silvestrov (2008) have already examined some of these cases, which we repeat for the reader's convenience.

    We further investigate the following σ-twisted derivations, and how they act in the different cases of mentioned polynomial algebras: the ordinary differential operator, the shifted difference operator, the Jackson q-derivation operator, the continuous q-difference operator, the Eulerian operator, the divided difference operator, and the nilpotent imaginary derivative operator. We also introduce a new, general, σ-twisted derivation operator, which is σ(t) as a polynomial of degree k.

    Download full text (pdf)
    fulltext
  • 25.
    Bergh, Petter Andreas
    et al.
    Institutt for Matematiske fag, NTNU, N-7491 Trondheim, Norway.
    Thompson, Peder
    Institutt for Matematiske fag, NTNU, N-7491 Trondheim, Norway.
    Matrix factorizations for self-orthogonal categories of modules2020In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 20, no 03, article id 2150037Article in journal (Refereed)
    Abstract [en]

    For a commutative ring S and self-orthogonal subcategory C of Mod(S), we consider matrix factorizations whose modules belong to C. Let f in S be a regular element. If f is M-regular for every M in C, we show there is a natural embedding of the homotopy category of C-factorizations of f into a corresponding homotopy category of totally acyclic complexes. Moreover, we prove this is an equivalence if C is the category of projective or flat-cotorsion S-modules. Dually, using divisibility in place of regularity, we observe there is a parallel equivalence when C is the category of injective S-modules. 

  • 26.
    Bergvall, Olof
    Stockholms universitet, Matematiska institutionen, Sweden.
    Cohomology of the moduli space of curves of genus three with level two structure2014Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In this thesis we investigate the moduli space M3[2] of curves of genus 3 equipped with a symplectic level 2 structure. In particular, we are interested in the cohomology of this space. We obtain cohomological information by decomposing M3[2] into a disjoint union of two natural subspaces, Q[2] and H3[2], and then making S7- resp. S8-equivariantpoint counts of each of these spaces separately.

  • 27.
    Bergvall, Olof
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden.
    Relations in the tautological ring of the universal curve2022In: Communications in analysis and geometry, ISSN 1019-8385, E-ISSN 1944-9992, Vol. 30, no 3, p. 501-522Article in journal (Refereed)
    Abstract [en]

    We bound the dimensions of the graded pieces of the tautological ring of the universal curve from below for genus up to 27 and from above for genus up to 9. As a consequence we obtain the precise structure of the tautological ring of the universal curve for genus up to 9. In particular, we see that it is Gorenstein for these genera.

  • 28.
    Bergvall, Olof
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics and Physics Mälardalen University Västerås Sweden.
    Gounelas, Frank
    Georg‐August‐Universität Göttingen Fakultät für Mathematik und Informatik Göttingen Germany.
    Cohomology of moduli spaces of Del Pezzo surfaces2022In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 295, no 12, p. 1-22Article in journal (Refereed)
    Abstract [en]

    We compute the rational Betti cohomology groups of the coarse moduli spaces of geometrically marked Del Pezzo surfaces of degree 3 and 4 as representations of the Weyl groups of the corresponding root systems. The proof uses a blend of methods from point counting over finite fields and techniques from arrangement complements.

  • 29. Brown, Michael K.
    et al.
    Miller, Claudia
    Thompson, Peder
    Univ Nebraska, Dept Math, Lincoln, NE 68588 USA .
    Walker, Mark E.
    Cyclic Adams operations2017In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 221, no 7, p. 1589-1613Article in journal (Refereed)
    Abstract [en]

    Let Q be a commutative, Noetherian ring and Z in Spec(Q) a closed subset. Define K_0^Z(Q) to be the Grothendieck group of those bounded complexes of finitely generated projective Q-modules that have homology supported on Z. We develop “cyclic” Adams operations on K_0^Z(Q) and we prove these operations satisfy the four axioms used by Gillet and Soulé in [9]. From this we recover a shorter proof of Serre’s Vanishing Conjecture. We also show our cyclic Adams operations agree with the Adams operations defined by Gillet and Soulé in certain cases. 

    Our definition of the cyclic Adams operators is inspired by a formula due to Atiyah [1]. They have also been introduced and studied before by Haution [10]. 

  • 30. Brown, Michael
    et al.
    Miller, Claudia
    Thompson, Peder
    exas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA .
    Walker, Mark
    Adams operations on matrix factorizations2017In: Algebra & Number Theory, ISSN 1937-0652, E-ISSN 1944-7833, Vol. 11, no 9, p. 2165-2192Article in journal (Refereed)
    Abstract [en]

    We define Adams operations on matrix factorizations, and we show these op- erations enjoy analogues of several key properties of the Adams operations on perfect complexes with support developed by Gillet and Soulé. As an application, we give a proof of a conjecture of Dao and Kurano concerning the vanishing of Hochster’s θ pairing. 

  • 31.
    Bäck, Per
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Multi-parameter formal deformations of ternary hom-Nambu-Lie algebras2020In: Lie Theory and its Applications in Physics / [ed] V. Dobrev, Singapore, 2020, Vol. 335, p. 455-460Conference paper (Refereed)
    Abstract [en]

    In this note, we introduce a notion of multi-parameter formal deformations of ternary hom-Nambu-Lie algebras. Within this framework, we construct formal deformations of the three-dimensional Jacobian determinantand of the cross-product in four-dimensional Euclidean space. We also conclude that the previously defined ternary q-Virasoro-Witt algebra is a formal deformation of the ternary Virasoro-Witt algebra.

  • 32.
    Bäck, Per
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Notes on formal deformations of quantum planes and universal enveloping algebras2019In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 1194, no 1, article id 012011Article in journal (Refereed)
    Abstract [en]

    In these notes, we introduce formal hom-associative deformations of the quantumplanes and the universal enveloping algebras of the two-dimensional non-abelian Lie algebras.We then show that these deformations induce formal hom-Lie deformations of the correspondingLie algebras constructed by using the commutator as bracket.

    Download full text (pdf)
    fulltext
  • 33.
    Bäck, Per
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    On Hom-associative Ore Extensions2022Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, we introduce and study hom-associative Ore extensions. These are non-unital, non-associative, non-commutative polynomial rings in which the associativity condition is “twisted” by an additive group homomorphism. In particular, they are examples of hom-associative algebras, and they generalize the classical non-commutative polynomial rings introduced by Ore known as Ore extensions to the non-unital, hom-associative setting. At the same time, when the twisted associativity condition is null, they also generalize to the general non-unital, non-associative setting. We deduce necessary and sufficient conditions for hom-associative Ore extensions to exist, and construct concrete examples thereof. These include hom-associative generalizations of the quantum plane, the universal enveloping algebra of the two-dimensional non-abelian Lie algebra, and the first Weyl algebra, to name a few. The aforementioned algebras turn out to be formal hom-associative deformations of their associative counterparts, the latter two which cannot be formally deformed in the associative setting. Moreover, these are all weakly unital algebras, and we provide a way of embedding any multiplicative, non-unital hom-associative algebra into a multiplicative, weakly unital hom-associative algebra. This generalizes the classical unitalization of non-unital, associative algebras. We then study the hom-associative Weyl algebras in arbitrary characteristic, classify them up to isomorphism, and in the zero characteristic case, we prove that an analogue of the Dixmier conjecture is true. We also study hom-modules over hom-associative rings, and by doing so, we are able to prove a Hilbert's basis theorem for hom-associative Ore extensions. Our theorem includes as special cases both the classical Hilbert's basis theorem for Ore extensions and a Hilbert's basis theorem for unital, non-associative Ore extensions. Last, we construct examples of both hom-associative and non-associative Ore extensions which are all Noetherian by our theorem.

    Download full text (pdf)
    fulltext
    Download (jpg)
    presentationsbild
  • 34.
    Bäck, Per
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Karaali, Gizem
    Pomona College in California, USA.
    The Algebra Detective: If Snape Is a Snake, Then P = K!2020In: Frontiers for Young Minds, E-ISSN 2296-6846, Vol. 8, article id 524026Article in journal (Other academic)
    Abstract [en]

    Algebra is often introduced as arithmetic done with letters. In this article, we follow this analogy and see where it takes us. We ask questions such as: If "SNAPE = SNAKE", can we conclude that "P = K"? Here is the spoiler: the path takes us into what mathematicians call group theory, a subfield of algebra that studies symmetry, and allows us to say interesting things about various languages like English and Swedish (and one very important fact about algebra itself).

  • 35.
    Bäck, Per
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Richter, Johan
    Blekinge tekniska högskola, Sweden.
    Hilbert's basis theorem and simplicity for non-associative skew Laurent polynomial rings and related ringsManuscript (preprint) (Other academic)
    Abstract [en]

    We introduce non-associative skew Laurent polynomial rings over unital, non-associative rings and prove simplicity results for these. We also generalize an already existing Hilbert’s basis theorem for non-associative Ore extensions and show that it implies a Hilbert’s basis theorem for non-associative skew Laurent polynomial rings. Moreover, we show that the above theorem can be extended to non-associative generalizations of both skew power series rings and skew Laurent series rings. We provide several examples to illustrate the applications of our results.

  • 36.
    Bäck, Per
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Richter, Johan
    Blekinge Tekniska Högskola.
    Hilbert's Basis Theorem for Non-associative and Hom-associative Ore Extensions2023In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 26, p. 1051-1065Article in journal (Refereed)
    Abstract [en]

    We prove a hom-associative version of Hilbert’s basis theorem, which includes as special cases both a non-associative version and the classical Hilbert’s basis theorem for associative Ore extensions. Along the way, we develop hom-module theory. We conclude with some examples of both non-associative and hom-associative Ore extensions which are all noetherian by our theorem.

  • 37.
    Bäck, Per
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Richter, Johan
    Blekinge Tekniska Högskola.
    On the hom-associative Weyl algebras2020In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 224, no 9Article in journal (Refereed)
    Abstract [en]

    The first (associative) Weyl algebra is formally rigid in the classical sense. In this paper, we show that it can however be formally deformed in a nontrivial way when considered as a so-called hom-associative algebra, and that this deformation preserves properties such as the commuter, while deforming others, such as the center, power associativity, the set of derivations, and some commutation relations. We then show that this deformation induces a formal deformation of the corresponding Lie algebra into what is known as a hom-Lie algebra, when using the commutator as bracket. We also prove that all homomorphisms between any two purely hom-associative Weyl algebras are in fact isomorphisms. In particular, all endomorphisms are automorphisms in this case, hence proving a hom-associative analogue of the Dixmier conjecture to hold true.

  • 38.
    Bäck, Per
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Richter, Johan
    Department of Mathematics and Natural Sciences, Blekinge Instituteof Technology.
    The hom-associative Weyl algebras in prime characteristic2022In: International Electronic Journal of Algebra, E-ISSN 1306-6048, Vol. 31, p. 203-229Article in journal (Refereed)
    Abstract [en]

    We introduce the first hom-associative Weyl algebras over a field of prime characteristic as a generalization of the first associative Weyl algebrain prime characteristic. First, we study properties of hom-associative algebras constructed from associative algebras by a general “twisting” procedure. Then, with the help of these results, we determine the commuter, center, nuclei, and set of derivations of the first hom-associative Weyl algebras. We also classify them up to isomorphism, and show, among other things, that all nonzero endomorphisms on them are injective, but not surjective. Last, we show that they can be described as a multi-parameter formal hom-associative deformation of the first associative Weyl algebra, and that this deformation induces a multi-parameter formal hom-Lie deformation of the corresponding Lie algebra, when using the commutator as bracket.

  • 39.
    Bäck, Per
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Richter, Johan
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Hom-associative Ore extensions2018In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 965, no 1, article id 012006Article in journal (Refereed)
    Abstract [en]

    We introduce hom-associative Ore extensions as non-associative, non-unital Ore extensions with a hom-associative multiplication, as well as give some necessary and sufficient conditions when such exist. Within this framework, we also construct a family of hom-associative Weyl algebras as generalizations of the classical analogue, and prove that they are simple.

  • 40.
    Bäck, Per
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Richter, Johan
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Hom-associative Ore extensions and weak unitalizations2018In: International Electronic Journal of Algebra, E-ISSN 1306-6048, Vol. 24, p. 174-194Article in journal (Refereed)
    Abstract [en]

    We introduce hom-associative Ore extensions as non-unital, nonassociative Ore extensions with a hom-associative multiplication, and give some necessary and sucient conditions when such exist. Within this framework, we construct families of hom-associative quantum planes, universal enveloping algebras of a Lie algebra, and Weyl algebras, all being hom-associative generalizations of their classical counterparts, as well as prove that the latter are simple. We also provide a way of embedding any multiplicative hom-associative algebra into a multiplicative, weakly unital hom-associative algebra, which we call a weak unitalization.

  • 41.
    Cantuba, Rafael Reno
    et al.
    De La Salle University, Malate, Manila, Philippines.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Lie polynomial characterization problems2020In: Algebraic Structures and Applications / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rancic, Springer Nature, 2020, Vol. 317, p. 593-601Chapter in book (Refereed)
    Abstract [en]

    We present a review of some results about Lie polynomials in finitely-generated associative algebras with defining relations that involve deformed commutation relations. Such algebras have arisen from various areas such as in the theory of quantum groups, of q-oscillators, of q-deformed Heisenberg algebras, of orthogonal polynomials, and even from algebraic combinatorics. The q-deformed Heisenberg-Weyl relation is so far the most successful setting for a Lie polynomial characterization problem. Both algebraic and operator-theoretic approaches have been found. We also discuss some partial results for other algebras related to quantum groups.

  • 42.
    Carlsen, Toke M.
    et al.
    Norwegian University of Science and Technology.
    Eilers, SorenUniversity of Copenhagen.Restorff, GunnarUniversity of the Faroe Islands.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication.
    Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 20122013Collection (editor) (Refereed)
  • 43.
    Carlsen, Toke Meier
    et al.
    University of Southern Denmark.
    Silvestrov, Sergei
    Lund University.
    On the Exel crossed product of topological covering maps2009In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, ISSN 0167-8019, Vol. 108, no 3, p. 573-583Article in journal (Refereed)
    Abstract [en]

    For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the associated crossed product C *-algebras C(X)⋊ α,ℒℕintroduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering map is topologically free; the canonical embedding of C(X) into C(X)⋊ α,ℒℕis a maximal abelian C *-subalgebra of C(X)⋊ α,ℒN; any nontrivial two sided ideal of C(X)⋊ α,ℒℕhas non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊ α,ℒℕis faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product C *-algebras of homeomorphism dynamical systems. 

  • 44.
    Christensen, Lars
    et al.
    Texas Tech University, USA.
    Estrada, Sergio
    University of Murcia, Spain.
    Thompson, Peder
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Five theorems on Gorenstein global dimensions2023In: Algebra and Coding Theory- Virtual Conference in Honor of Tariq Rizvi Noncommutative Rings and their Applications VII, 2021 and Virtual Conference on Quadratic Forms, Rings and Codes, 2021, American Mathematical Society (AMS), 2023, p. 67-78Conference paper (Refereed)
    Abstract [en]

    We expand on two existing characterizations of rings of Gorenstein (weak) global dimension zero and give two new characterizations of rings of finite Gorenstein (weak) global dimension. We also include the answer to a question of Y. Xiang on Gorenstein weak global dimension of group rings. 

  • 45.
    Christensen, Lars
    et al.
    Texas Tech Univ, Lubbock, TX 79409 USA .
    Estrada, Sergio
    Univ Murcia, Murcia 30100, Spain.
    Thompson, Peder
    Norwegian Univ Sci & Technol, N-7491 Trondheim, Norway.
    Homotopy categories of totally acyclic complexes with applications to the flat–cotorsion theory2020In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, p. 99-118Article in journal (Refereed)
    Abstract [en]

    We introduce a notion of total acyclicity associated to a subcategory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius category, whose induced stable category is equivalent to the homotopy category of totally acyclic complexes. Applied to the flat–cotorsion theory over a coherent ring, this provides a new description of the category of cotorsion Gorenstein flat modules; one that puts it on equal footing with the category of Gorenstein projective modules. 

  • 46.
    Christensen, Lars Winther
    et al.
    Department of Mathematics and Statistics, Texas Tech University , Lubbock, TX 79409, USA.
    Ding, Nanqing
    Department of Mathematics, Nanjing University , Nanjing 210093, China.
    Estrada, Sergio
    Departamento de Matemáticas, Universidad de Murcia , Murcia 30100, Spain.
    Hu, Jiangsheng
    School of Mathematics and Physics, Jiangsu University of Technology , Changzhou 213001, China.
    Li, Huanhuan
    School of Mathematics and Statistics, Xidian University , Xi’an 710071, China.
    Thompson, Peder
    Mathematics Department Norwegian University of Science and Technology , 7491 Trondheim, Norway;Niagara University, Niagara University , NY 14109, USA.
    The Singularity Category Of An Exact Category Applied To Characterize Gorenstein Schemes2023In: Quarterly Journal of Mathematics, ISSN 0033-5606, E-ISSN 1464-3847, Vol. 74, no 1, p. 1-27Article in journal (Refereed)
    Abstract [en]

    We construct a non-affine analogue of the singularity category of a Gorenstein local ring. With this, Buchweitz’s classic equivalence of three triangulated categories over a Gorenstein local ring has been generalized to schemes, a project started by Murfet and Salarian more than ten years ago. Our construction originates in a framework we develop for singularity categories of exact categories. As an application of this framework in the non-commutative setting, we characterize rings of finite finitistic dimension. 

  • 47.
    Christensen, Lars Winther
    et al.
    Texas Tech Univ, Lubbock, TX 79409 USA.
    Estrada, Sergio
    Univ Murcia, Murcia 30100, Spain.
    Liang, Li
    Lanzhou Jiaotong Univ, Lanzhou 730070, Peoples R China.
    Thompson, Peder
    Norwegian Univ Sci & Technol, N-7491 Trondheim, Norway.
    Wu, Dejun
    Lanzhou Univ Technol, Lanzhou 730050, Peoples R China.
    Yang, Gang
    Lanzhou Jiaotong Univ, Lanzhou 730070, Peoples R China.
    A refinement of Gorenstein flat dimension via the flat–cotorsion theory2021In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 567, p. 346-370Article in journal (Refereed)
    Abstract [en]

    We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring—the Gorenstein flat- cotorsion dimension—and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological di- mension without extra assumptions on the ring. Crucially, we show that it coincides with the Gorenstein flat dimension for complexes where the latter is finite, and for complexes over right coherent rings—the setting where the Gorenstein flat dimension is known to behave as expected.

  • 48.
    Christensen, Lars Winther
    et al.
    Texas Tech University Lubbock TX 79409 U.S.A..
    Estrada, Sergio
    Universidad de Murcia Murcia 30100 Spain.
    Thompson, Peder
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Gorenstein weak global dimension is symmetric2021In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 294, no 11, p. 2121-2128Article in journal (Refereed)
    Abstract [en]

    We study the Gorenstein weak global dimension of associative rings and its relation to the Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein weak global dimension is a left-right symmetric invariant – just like the (absolute) weak global dimension. 

  • 49.
    Christensen, Lars Winther
    et al.
    Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA.
    Estrada, Sergio
    Univ Murcia, Dept Matemat, Murcia 30100, Spain.
    Thompson, Peder
    Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway.
    The stable category of Gorenstein flat sheaves on a noetherian scheme2020In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 149, no 2, p. 525-538Article in journal (Refereed)
    Abstract [en]

    For a semiseparated noetherian scheme, we show that the cate- gory of cotorsion Gorenstein flat quasi-coherent sheaves is Frobenius and a natural non-affine analogue of the category of Gorenstein projective modules over a noetherian ring. We show that this coheres perfectly with the work of Murfet and Salarian that identifies the pure derived category of F-totally acy- clic complexes of flat quasi-coherent sheaves as the natural non-affine analogue of the homotopy category of totally acyclic complexes of projective modules. 

  • 50.
    Christensen, Lars Winther
    et al.
    Texas Tech University, Lubbock, USA.
    Thompson, Peder
    Texas Tech Univ, Dept Math & Stat, 1108 Mem Circle, Lubbock, TX 79409 USA.
    Pure-minimal chain complexes2019In: Rendiconti del Seminario Matematico della Universita di Padova, ISSN 0041-8994, E-ISSN 2240-2926, Vol. 142, p. 41-67Article in journal (Refereed)
    Abstract [en]

    We introduce a notion of pure-minimality for chain complexes of modules and show that it coincides with (homotopic) minimality in standard settings, while being a more useful notion for complexes of flat modules. As applications, we characterize von Neumann regular rings and left perfect rings. 

1234 1 - 50 of 192
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf