Sergei Silvestrov | Mälardalen University (original) (raw)
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Papers by Sergei Silvestrov
arXiv (Cornell University), May 4, 2021
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arXiv (Cornell University), Jul 9, 2004
We study the relation between representations of color Lie algebras and their cocycle deformation... more We study the relation between representations of color Lie algebras and their cocycle deformations. In particular, we obtain a class of FCR-algebras, which are related to some color Lie algebras. As an application, we compute all the finite-dimensional simple representations of the color Lie algebra sl2csl_2^csl2c.
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International Journal of Mathematics Trends and Technology, Feb 25, 2014
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Journal of physics, Feb 10, 2005
We propose a new kind of two-parameter (p, q)-deformed Heisenberg and parabose algebra, which red... more We propose a new kind of two-parameter (p, q)-deformed Heisenberg and parabose algebra, which reduces to the Heisenberg algebra for the p = 1 case and to parabose algebra for q = -1 case. Corresponding to the two-parameter deformed oscillator, we also introduce a new kind of (p, q)-deformed derivative which relates to the ordinary derivative and q-deformed derivative in an explicit manner. We study the structure of Fock-like space of the new (p, q)-deformed oscillators and derive a formal solution for the eigenvalue equation of the Hamiltonian.
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Springer proceedings in mathematics & statistics, 2020
The aim of the present article is to review the current progress on Hom-Gerstenhaber algebras and... more The aim of the present article is to review the current progress on Hom-Gerstenhaber algebras and Hom-Lie algebroids. There are two different definitions of Hom-Lie algebroids. The modification was made in the original definition to consider some essential results on Hom-Lie algebroids and discuss some new examples. However, it turns out that for such results such a modification is not required. There are several attempts on defining representations and cohomology of Hom-Lie algebroids. As expected from the case of Hom-Lie algebras, there is no unique cohomology for Hom-Lie algebroids. We discuss about representations and cohomology of Hom-Lie algebroids that yields a differential calculus and dual description for Hom-Lie algebroids. Later on, we summarise the relationship between Hom-Lie algebroids and Hom-Gerstenhaber algebras.
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Springer proceedings in mathematics & statistics, 2020
In this paper the universal enveloping algebra of color hom-Lie algebras is studied. A constructi... more 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 Poincare–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.
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arXiv (Cornell University), Feb 28, 2018
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arXiv (Cornell University), Oct 5, 2020
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arXiv (Cornell University), May 7, 2022
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Turkish Journal of Mathematics, Jan 18, 2019
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Journal of Generalized Lie Theory and Applications, 2009
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Acta Applicandae Mathematicae, Jul 16, 2008
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arXiv (Cornell University), Apr 2, 2023
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Springer proceedings in mathematics & statistics, 2020
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Operators and Matrices, 2011
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arXiv (Cornell University), Dec 3, 2019
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arXiv (Cornell University), Oct 18, 2020
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arXiv (Cornell University), Oct 25, 2021
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arXiv (Cornell University), May 4, 2021
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arXiv (Cornell University), Jul 9, 2004
We study the relation between representations of color Lie algebras and their cocycle deformation... more We study the relation between representations of color Lie algebras and their cocycle deformations. In particular, we obtain a class of FCR-algebras, which are related to some color Lie algebras. As an application, we compute all the finite-dimensional simple representations of the color Lie algebra sl2csl_2^csl2c.
Bookmarks Related papers MentionsView impact
International Journal of Mathematics Trends and Technology, Feb 25, 2014
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Journal of physics, Feb 10, 2005
We propose a new kind of two-parameter (p, q)-deformed Heisenberg and parabose algebra, which red... more We propose a new kind of two-parameter (p, q)-deformed Heisenberg and parabose algebra, which reduces to the Heisenberg algebra for the p = 1 case and to parabose algebra for q = -1 case. Corresponding to the two-parameter deformed oscillator, we also introduce a new kind of (p, q)-deformed derivative which relates to the ordinary derivative and q-deformed derivative in an explicit manner. We study the structure of Fock-like space of the new (p, q)-deformed oscillators and derive a formal solution for the eigenvalue equation of the Hamiltonian.
Bookmarks Related papers MentionsView impact
Springer proceedings in mathematics & statistics, 2020
The aim of the present article is to review the current progress on Hom-Gerstenhaber algebras and... more The aim of the present article is to review the current progress on Hom-Gerstenhaber algebras and Hom-Lie algebroids. There are two different definitions of Hom-Lie algebroids. The modification was made in the original definition to consider some essential results on Hom-Lie algebroids and discuss some new examples. However, it turns out that for such results such a modification is not required. There are several attempts on defining representations and cohomology of Hom-Lie algebroids. As expected from the case of Hom-Lie algebras, there is no unique cohomology for Hom-Lie algebroids. We discuss about representations and cohomology of Hom-Lie algebroids that yields a differential calculus and dual description for Hom-Lie algebroids. Later on, we summarise the relationship between Hom-Lie algebroids and Hom-Gerstenhaber algebras.
Bookmarks Related papers MentionsView impact
Springer proceedings in mathematics & statistics, 2020
In this paper the universal enveloping algebra of color hom-Lie algebras is studied. A constructi... more 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 Poincare–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.
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arXiv (Cornell University), Feb 28, 2018
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arXiv (Cornell University), Oct 5, 2020
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arXiv (Cornell University), May 7, 2022
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Turkish Journal of Mathematics, Jan 18, 2019
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Journal of Generalized Lie Theory and Applications, 2009
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Acta Applicandae Mathematicae, Jul 16, 2008
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arXiv (Cornell University), Apr 2, 2023
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Springer proceedings in mathematics & statistics, 2020
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Operators and Matrices, 2011
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arXiv (Cornell University), Dec 3, 2019
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arXiv (Cornell University), Oct 18, 2020
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arXiv (Cornell University), Oct 25, 2021
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