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  • 1.
    Bäck, Per
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Hom-associative Ore extensions2018Inngår i: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 965, nr 1, artikkel-id 012006Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 2.
    Bäck, Per
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Hom-associative Ore extensions and weak unitalizations2018Inngår i: International Electronic Journal of Algebra, ISSN 1306-6048, E-ISSN 1306-6048, Vol. 24, s. 174-194Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 3.
    Mosson, R.
    et al.
    Karolinska Institutet.
    Augustsson, H.
    Karolinska Institutet.
    Bäck, A.
    Karolinska Institutet.
    Åhström, M.
    Stockholm County Council.
    von Thiele Schwarz, Ulrica
    Mälardalens högskola, Akademin för hälsa, vård och välfärd, Hälsa och välfärd. Stockholm County Council.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Karolinska Institutet.
    Gunnarsson, M.
    Stockholm County Council.
    Hasson, H.
    Stockholm County Council.
    Building implementation capacity (BIC): A longitudinal mixed methods evaluation of a team intervention2019Inngår i: BMC Health Services Research, ISSN 1472-6963, E-ISSN 1472-6963, Vol. 19, nr 1, artikkel-id 287Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Background: Managers and professionals in health and social care are required to implement evidence-based methods. Despite this, they generally lack training in implementation. In clinical settings, implementation is often a team effort, so it calls for team training. The aim of this study was to evaluate the effects of the Building Implementation Capacity (BIC) intervention that targets teams of professionals, including their managers. Methods: A non-randomized design was used, with two intervention cases (each consisting of two groups). The longitudinal, mixed-methods evaluation included pre-post and workshop-evaluation questionnaires, and interviews following Kirkpatrick's four-level evaluation framework. The intervention was delivered in five workshops, using a systematic implementation method with exercises and practical working materials. To improve transfer of training, the teams' managers were included. Practical experiences were combined with theoretical knowledge, social interactions, reflections, and peer support. Results: Overall, the participants were satisfied with the intervention (first level), and all groups increased their self-rated implementation knowledge (second level). The qualitative results indicated that most participants applied what they had learned by enacting new implementation behaviors (third level). However, they only partially applied the implementation method, as they did not use the planned systematic approach. A few changes in organizational results occurred (fourth level). Conclusions: The intervention had positive effects with regard to the first two levels of the evaluation model; that is, the participants were satisfied with the intervention and improved their knowledge and skills. Some positive changes also occurred on the third level (behaviors) and fourth level (organizational results), but these were not as clear as the results for the first two levels. This highlights the fact that further optimization is needed to improve transfer of training when building teams' implementation capacity. In addition to considering the design of such interventions, the organizational context and the participants' characteristics may also need to be considered to maximize the chances that the learned skills will be successfully transferred to behaviors.

  • 4.
    Musonda, John
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics and Statistics, University of Zambia, Zambia.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Reordering in a multi-parametric family of algebras2019Inngår i: Journal of Physics: Conference Series, Institute of Physics Publishing , 2019, nr 1Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This article is devoted to a multi-parametric family of associative complex algebras defined by commutation relations associated with group or semigroup actions of dynamical systems and iterated function systems. General reordering and nested commutator formulas for arbitrary elements in these families are presented, generalizing some well-known results in mathematics and physics. A generalization of this family in three generators is also considered.

  • 5.
    Nystedt, Patrik
    et al.
    Högskolan Väst, Sweden.
    Öinert, Johan
    Blekinge Tekniska Högskola, Sweden.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Non-associative Ore extensions2018Inngår i: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 224, nr 1, s. 263-292Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce non-associative Ore extensions, S = R[X; σ, δ], for any nonassociative unital ring R and any additive maps σ, δ: R → R satisfying σ(1) = 1 and δ(1) = 0. In the special case when δ is either left or right Rδ-linear, where Rδ = ker(δ), and R is δ-simple, i.e. {0} and R are the only δ-invariant ideals of R, we determine the ideal structure of the nonassociative differential polynomial ring D = R[X; idR, δ]. Namely, in that case, we show that all non-zero ideals of D are generated by monic polynomials in the center Z(D) of D. We also show that Z(D) = Rδ[p] for a monic p ∈ Rδ[X], unique up to addition of elements from Z(R)δ. Thereby, we generalize classical results by Amitsur on differential polynomial rings defined by derivations on associative and simple rings. Furthermore, we use the ideal structure of D to show that D is simple if and only if R is δ-simple and Z(D) equals the field Rδ ∩ Z(R). This provides us with a non-associative generalization of a result by Öinert, Richter and Silvestrov. This result is in turn used to show a non-associative version of a classical result by Jordan concerning simplicity of D in the cases when the characteristic of the field Rδ ∩ Z(R) is either zero or a prime. We use our findings to show simplicity results for both non-associative versions of Weyl algebras and non-associative differential polynomial rings defined by monoid/group actions on compact Hausdorff spaces. 

  • 6.
    Nystedt, Patrik
    et al.
    Department of Engineering Science, University West, Trollhättan, Sweden.
    Öinert, Johan
    Blekinge Tekniska Högskola.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Simplicity of Ore monoid rings2019Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 530, s. 69-85Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Given a non-associative unital ring R, a monoid G and a set π of additive maps R→R, we introduce the Ore monoid ring R[π;G], and, in a special case, the differential monoid ring. We show that these structures generalize, in a natural way, not only the classical Ore extensions and differential polynomial rings, but also the constructions, introduced by Cojuhari, defined by so-called D-structures π. Moreover, for commutative monoids, we give necessary and sufficient conditions for differential monoid rings to be simple. We use this in a special case to obtain new and shorter proofs of classical simplicity results for differential polynomial rings in several variables previously obtained by Voskoglou and Malm by other means. We also give examples of new Ore-like structures defined by finite commutative monoids.

  • 7.
    Ongong'A, Elvice
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. University of Nairobi, Nairobi, Kenya .
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Classification of 3-dimensional Hom-Lie algebras2019Inngår i: Journal of Physics: Conference Series, Institute of Physics Publishing , 2019, nr 1Konferansepaper (Fagfellevurdert)
    Abstract [en]

    For any n-dimensional Hom-Lie algebra, a system of polynomial equations is obtained from the Hom-Jacobi identity, containing both structure constants of the skew-symmetric bilinear map and constants describing the twisting linear endomorphism. The equations are linear in the constants representing the endomorphism and non-linear in the structure constants. The space of possible endomorphisms has minimum dimension 6, and we describe the possible endomorphisms in that case. We further give families of 3-dimensional Hom-Lie algebras arising from a general nilpotent linear endomorphism constructed upto isomorphism.

  • 8.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Lund University, Sweden.
    Burchnall-Chaundy Theory for Ore Extensions2014Inngår i: Algebra, Geometry and Mathematical Physics / [ed] Makhlouf, Abdenacer; Paal, Eugen; Silvestrov, Sergei D.; Stolin, Alexander, Springer Berlin Heidelberg , 2014, Vol. 85, s. 61-70Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    We begin by reviewing a classical result on the algebraic dependence of commuting elements in the Weyl algebra. We proceed by describing generalizations of this result to various classes of Ore extensions, including both results that are already known and one new result.

  • 9.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Centralizers and Pseudo-Degree Functions2016Inngår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Silvestrov, Sergei and Rančić, Milica, Springer, 2016, s. 65-73Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    This paper generalizes a proof of certain results by Hellström and Silvestrov on centralizers in graded algebras. We study centralizers in certain algebras with valuations. We prove that the centralizer of an element in these algebras is a free module over a certain ring. Under further assumptions we obtain that the centralizer is also commutative.

  • 10.
    Richter, Johan
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Centralizers in Ore extensions over polynomial rings2014Inngår i: International Electronic Journal of Algebra, ISSN 1306-6048, E-ISSN 1306-6048, Vol. 15, s. 15s. 196-207Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we consider centralizers of single elements in Ore extensions of the ring of polynomials in one variable over a field. We show that they are commutative and finitely generated as an algebra. We also show that for certain classes of elements their centralizer is singly generated as an algebra.

  • 11.
    Richter, Johan
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Computing Burchnall–Chaundy Polynomials with Determinants2016Inngår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov, Milica Rančić, Springer, 2016, s. 57-63Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    In this expository paper we discuss a way of computing the Burchnall-Chaundy polynomial of two commuting differential operators using a determinant.We describe how the algorithm can be generalized to general Ore extensions, andwhich properties of the algorithm that are preserved.

  • 12.
    Richter, Johan
    et al.
    Lund University.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation. Lund University.
    On algebraic curves for commuting elements in $q$-Heisenberg algebras2009Inngår i: Journal of Generalized Lie Theory and Applications, ISSN 1736-5279, E-ISSN 1736-4337, Vol. 3, nr 4, s. 321-328Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the present article we continue investigating the algebraic dependence of commutingelements in q-deformed Heisenberg algebras. We provide a simple proof that the0-chain subalgebra is a maximal commutative subalgebra when q is of free type and thatit coincides with the centralizer (commutant) of any one of its elements dierent fromthe scalar multiples of the unity. We review the Burchnall-Chaundy-type construction forproving algebraic dependence and obtaining corresponding algebraic curves for commutingelements in the q-deformed Heisenberg algebra by computing a certain determinantwith entries depending on two commuting variables and one of the generators. The coecients in front of the powers of the generator in the expansion of the determinant arepolynomials in the two variables dening some algebraic curves and annihilating the twocommuting elements. We show that for the elements from the 0-chain subalgebra exactlyone algebraic curve arises in the expansion of the determinant. Finally, we present severalexamples of computation of such algebraic curves and also make some observations onthe properties of these curves.

  • 13.
    Richter, Johan
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Ssembatya, Vincent
    Makerere University.
    Tumwesigye, Alex
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Makerere University.
    Crossed Product Algebras for Piece-Wise Constant Functions2016Inngår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rančić, Springer, 2016Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    In this paper we consider algebras of functions that are constant on the sets of a partition. We describe the crossed product algebras of the mentioned algebras with Z. We show that the function algebra is isomorphic to the algebra of all functions on some set. We also describe the commutant of the function algebra and finish by giving an example of piece-wise constant functions on a real line.

  • 14.
    Richter, Johan
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Tumwesigye, Alex
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Makerere University.
    Commutants in Crossed Product Algebras for Piece-Wise Constant Functions2016Inngår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and OptimizationEditors / [ed] Sergei Silvestrov; Milica Rančić, Springer, 2016, s. 95-108Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    In this paper we consider crossed product algebras of algebras of piecewiseconstant functions on the real line with Z. For an increasing sequence of algebras (in which case the commutants form a decreasing sequence), we describe the set difference between the corresponding commutants.

  • 15.
    Tumwesigye, Alex Behakanira
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Ore extensions of function algebras2018Konferansepaper (Annet (populærvitenskap, debatt, mm))
  • 16.
    Tumwesigye, Alex
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Makerere University.
    Richter, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Commutants in crossed products for algebras of piecewise constant functions on the real lineManuskript (preprint) (Annet (populærvitenskap, debatt, mm))
1 - 16 of 16
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