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Silvestrov, Sergei, ProfessorORCID iD iconorcid.org/0000-0003-4554-6528
Alternative names
Publications (10 of 265) Show all publications
Djinja, D., Silvestrov, S. & Tumwesigye, A. B. (2024). Linear integral operators on Lp spaces representing polynomial covariance type commutation relations. Afrika Matematika, 35(1), Article ID 18.
Open this publication in new window or tab >>Linear integral operators on Lp spaces representing polynomial covariance type commutation relations
2024 (English)In: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 35, no 1, article id 18Article in journal (Refereed) Published
Abstract [en]

In this work, we present methods for constructing representations of polynomial covariance type commutation relations AB= BF(A) by linear integral operators in Banach spaces Lp . We derive necessary and sufficient conditions on the kernel functions for the integral operators to satisfy the covariance type commutation relation for general polynomials F, as well as for important cases, when F is arbitrary affine or quadratic polynomial, or arbitrary monomial of any degree. Using the obtained general conditions on the kernels, we construct concrete examples of representations of the covariance type commutation relations by integral operators on Lp . Also, we derive useful general reordering formulas for the integral operators representing the covariance type commutation relations, in terms of the kernel functions.

Keywords
Covariance commutation relations, Integral operators
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:mdh:diva-65358 (URN)10.1007/s13370-023-01153-6 (DOI)001137951800001 ()2-s2.0-85181759228 (Scopus ID)
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2024-01-17 Created: 2024-01-17 Last updated: 2024-01-24Bibliographically approved
Laraiedh, I. & Silvestrov, S. (2023). Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman Color Hom-Algebras. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019 (pp. 613-659). Springer
Open this publication in new window or tab >>Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman Color Hom-Algebras
2023 (English)In: 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. 613-659Conference paper, Published paper (Refereed)
Abstract [en]

The main feature of color Hom-algebras is that the identities defining the structures are twisted by even linear maps. The purpose of this paper is to introduce and give some constructions of admissible Hom-Novikov-Poisson color Hom-algebras and Hom-Gelfand-Dorfman color Hom-algebras. Their bimodules and matched pairs are defined and the relevant properties and theorems are given. Also, the connections between Hom-Novikov-Poisson color Hom-algebras and Hom-Gelfand-Dorfman color Hom-algebras are proved. Furthermore, we show that the class of admissible Hom-Novikov-Poisson color Hom-algebras is closed under tensor product.

Place, publisher, year, edition, pages
Springer, 2023
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords
BiHom-Lie algebra, BiHom-Lie derivation, Derivation, Centroid
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64599 (URN)10.1007/978-3-031-32009-5_22 (DOI)2-s2.0-85174438979 (Scopus ID)9783031320088 (ISBN)
Conference
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Available from: 2023-10-30 Created: 2023-10-30 Last updated: 2023-12-27Bibliographically approved
Arfa, A., Saadaoui, N. & Silvestrov, S. (2023). Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz Algebras. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019 (pp. 33-60). Springer
Open this publication in new window or tab >>Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz Algebras
2023 (English)In: 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, Published 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.

Place, publisher, year, edition, pages
Springer, 2023
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords
Hom-Lie superalgebra, Hom-Leibniz superalgebra, Centroid, Derivation
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64617 (URN)10.1007/978-3-031-32009-5_3 (DOI)2-s2.0-85174444980 (Scopus ID)9783031320088 (ISBN)
Conference
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Available from: 2023-10-26 Created: 2023-10-26 Last updated: 2023-12-28Bibliographically approved
Armakan, A. & Silvestrov, S. (2023). Color Hom-Lie Algebras, Color Hom-Leibniz Algebras and Color Omni-Hom-Lie Algebras. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019 (pp. 61-79). Springer
Open this publication in new window or tab >>Color Hom-Lie Algebras, Color Hom-Leibniz Algebras and Color Omni-Hom-Lie Algebras
2023 (English)In: 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, Published 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.

Place, publisher, year, edition, pages
Springer, 2023
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords
Color Hom-Lie algebras, Color Omni-Hom-Lie algebra, Color Hom-Leibniz algebra
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64613 (URN)10.1007/978-3-031-32009-5_4 (DOI)2-s2.0-85174444260 (Scopus ID)9783031320088 (ISBN)
Conference
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Available from: 2023-10-27 Created: 2023-10-27 Last updated: 2023-12-28Bibliographically approved
Silvestrov, S. & Tumwesigye, A. B. (2023). Commutants in Crossed Products for Piecewise Constant Function Algebras Related to Multiresolution Analysis. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019 (pp. 709-724). Springer
Open this publication in new window or tab >>Commutants in Crossed Products for Piecewise Constant Function Algebras Related to Multiresolution Analysis
2023 (English)In: 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. 709-724Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we consider crossed product algebras of piecewise constant function algebras on the real line that arise in multiresolution analysis. Such algebras form an increasing sequence of algebras of functions on the real line. We derive conditions under which these algebras are invariant under a bijection on the real line, in which case we get an increasing sequence of crossed product algebras. We then give a comparison of commutants (centralizers) in a number of cases.

Place, publisher, year, edition, pages
Springer, 2023
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords
Crossed product algebra, Multiresolution analysis, Commutant
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64594 (URN)10.1007/978-3-031-32009-5_25 (DOI)2-s2.0-85174444965 (Scopus ID)9783031320088 (ISBN)
Conference
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Available from: 2023-10-30 Created: 2023-10-30 Last updated: 2023-12-27Bibliographically approved
Harrathi, F., Hounkonnou, M. N., Mabrouk, S. & Silvestrov, S. (2023). Construction and Characterization of n-Ary Hom-Bialgebras and n-Ary Infinitesimal Hom-Bialgebras. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019 (pp. 399-428). Springer, 426
Open this publication in new window or tab >>Construction and Characterization of n-Ary Hom-Bialgebras and n-Ary Infinitesimal Hom-Bialgebras
2023 (English)In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, Vol. 426, p. 399-428Conference paper, Published paper (Refereed)
Abstract [en]

Constructions of n-ary bialgebras and n-ary infinitesimal bialgebras of associative type and their hom-analogs, generalizing the hom-bialgebras and infinitesimal hom-bialgebras are investigated. Main algebraic characteristics of n-ary totally, n-ary weak totally, n-ary partially and n-ary alternate partially associative algebras and bialgebras, and their hom-counterparts are described. Particular cases of ternary algebras are given as illustration.

Place, publisher, year, edition, pages
Springer, 2023
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords
Hom-associative algebras, Infinitesimal Hom-bialgebras, n-ary Hom-bialgebras of associative type, n-ary infinitesimal Hom-bialgebras of associative type
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64611 (URN)10.1007/978-3-031-32009-5_16 (DOI)2-s2.0-85174450339 (Scopus ID)9783031320088 (ISBN)
Conference
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Available from: 2023-10-27 Created: 2023-10-27 Last updated: 2023-12-27Bibliographically approved
Attari Polsangi, A. R., Farhangdoost, M. R. & Silvestrov, S. (2023). Decomposition of Complete Color Hom-Lie Algebras. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019 (pp. 101-120). Springer
Open this publication in new window or tab >>Decomposition of Complete Color Hom-Lie Algebras
2023 (English)In: 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, Published 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.

Place, publisher, year, edition, pages
Springer, 2023
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords
Color hom-Lie algebra, Complete color hom-Lie algebra, Simple color hom-Lie algebra
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64612 (URN)10.1007/978-3-031-32009-5_6 (DOI)2-s2.0-85174447313 (Scopus ID)9783031320088 (ISBN)
Conference
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Available from: 2023-10-27 Created: 2023-10-27 Last updated: 2023-12-28Bibliographically approved
García Butenegro, G., Kitouni, A. & Silvestrov, S. (2023). Divisibility in Hom-Algebras, Single-Element Properties in Non-associative Algebras and Twisted Derivations. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures — From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019 (pp. 303-337). Springer
Open this publication in new window or tab >>Divisibility in Hom-Algebras, Single-Element Properties in Non-associative Algebras and Twisted Derivations
2023 (English)In: 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. 303-337Conference paper, Published paper (Refereed)
Abstract [en]

We compare and examine the influence of Hom-associativity, involving a linear map twisting the associativity axiom, on fundamental aspects important in study of Hom-algebras and (σ,τ)-derivations satisfying a (σ,τ)-twisted Leibniz product rule in connection to Hom-algebra structures. As divisibility may be not transitive in general not necessarily associative algebras, we explore factorization properties of elements in Hom-associative algebras, specially related to zero divisors, and develop an α-deformed divisibility sequence, formulated in terms of linear operators. We explore effects of the twisting maps σ and τ on the whole space of twisted derivations, unfold some partial results on the structure of (σ,τ)-derivations on arbitrary algebras based on a pivot element related to σ and τ and examine how general an algebra can be while preserving certain well-known relations between (σ,τ)-derivations. Furthermore, new more general axioms of Hom-associativity, Hom-alternativity and Hom-flexibility modulo kernel of a derivation are introduced leading to new classes of Hom-algebras motivated by (σ,τ)-Leibniz rule over multiplicative maps σ and τ and study of twisted derivations in arbitrary algebras and their connections to Hom-algebra structures.

Place, publisher, year, edition, pages
Springer, 2023
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords
Hom-algebra, Divisor, Twisted derivation
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64607 (URN)10.1007/978-3-031-32009-5_13 (DOI)2-s2.0-85174441305 (Scopus ID)9783031320088 (ISBN)
Conference
International Conference on Stochastic Processes and Algebraic Structures — From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Available from: 2023-10-27 Created: 2023-10-27 Last updated: 2023-12-28Bibliographically approved
Hounkonnou, M. N., Houndedji, G. D. & Silvestrov, S. (2023). Double Constructions of BiHom-Frobenius Algebras. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October, 2023 (pp. 477-523). Springer
Open this publication in new window or tab >>Double Constructions of BiHom-Frobenius Algebras
2023 (English)In: 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. 477-523Conference paper, Published paper (Refereed)
Abstract [en]

This paper addresses a Hom-associative algebra built as a direct sum of a given Hom-associative algebra (A, ·, α) and its dual (A, ∘, α), endowed with a non-degenerate symmetric bilinear form B, where · and ∘ are the products defined on A and A, respectively, and α and α stand for the corresponding algebra homomorphisms. Such a double construction, also called Hom-Frobenius algebra, is interpreted in terms of an infinitesimal Hom-bialgebra. The same procedure is applied to characterize the double construction of biHom-associative algebras, also called biHom-Frobenius algebra. Finally, a double construction of Hom-dendriform algebras, also called double construction of Connes cocycle or symplectic Hom-associative algebra, is performed. Besides, the concept of biHom-dendriform algebras is introduced and discussed. Their bimodules and matched pairs are also constructed, and related relevant properties.

Place, publisher, year, edition, pages
Springer, 2023
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords
Hom-associative algebra, BiHom-associative algebra, BiHom-Frobenius algebra, BiHom-dendriform algebra
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64620 (URN)10.1007/978-3-031-32009-5_18 (DOI)2-s2.0-85174448582 (Scopus ID)9783031320088 (ISBN)
Conference
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October, 2023
Available from: 2023-10-26 Created: 2023-10-26 Last updated: 2023-12-28Bibliographically approved
García Butenegro, G. & Silvestrov, S. (2023). Elduque-Myung Type Mutations of Hom-algebras. In: Hounkonnou, M.N., Mitrović, M., Abbas, M., Khan, M (Ed.), Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures: (pp. 295-330). Springer
Open this publication in new window or tab >>Elduque-Myung Type Mutations of Hom-algebras
2023 (English)In: Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures / [ed] Hounkonnou, M.N., Mitrović, M., Abbas, M., Khan, M, Springer, 2023, p. 295-330Chapter in book (Refereed)
Abstract [en]

Elduque-Myung type mutations of general, possibly non-associative, algebras and of several classes of Hom-algebras are explored. Several extensions of the results from scalar and non-scalar mutations of associative algebras to mutations of non-associative algebras and of several kinds of hom-algebras of hom-associative type are obtained, including general conditions, in terms of Hom-associators, commutators and general mutation elements (mutations parameters), for mutated Hom-algebras or non-associative algebras to be Hom-associative, Hom-flexible, 3-Hom-Power associative, as well as results on reductions of double parameter mutations to single parameter mutations in algebras and Hom-algebras. Several formulas for mutations of associative algebras are extended to arbitrary possibly non-associative algebras and Hom-algebras.

Place, publisher, year, edition, pages
Springer, 2023
Series
STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, ISSN 2520193X
Keywords
Mutation, Non-associative algebra, Hom-algebra, Hom-associator
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-65044 (URN)10.1007/978-3-031-39334-1_7 (DOI)2-s2.0-85180645957 (Scopus ID)978-3-031-39333-4 (ISBN)978-3-031-39334-1 (ISBN)
Available from: 2023-12-15 Created: 2023-12-15 Last updated: 2024-01-23Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-4554-6528