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Papers by Sergei Silvestrov

Research paper thumbnail of Constructions of BiHom-X algebras and bimodules of some BiHom-dialgebras

arXiv (Cornell University), May 4, 2021

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Research paper thumbnail of Matrix monotone functions on C*-algebras

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Research paper thumbnail of HNN-extension of involutive multiplicative Hom-Lie algebras

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Research paper thumbnail of A Note on Color Lie Algebras

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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Research paper thumbnail of New Paranormed Sequence Spaces l∞(p,λ) , c(p,λ) and c0(p,λ) Generated by an Infinite Matrix

International Journal of Mathematics Trends and Technology, Feb 25, 2014

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Research paper thumbnail of A new kind of two-parameter deformation of Heisenberg and parabose algebras and related deformed derivative

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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Research paper thumbnail of A Review on Hom-Gerstenhaber Algebras and Hom-Lie Algebroids

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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Research paper thumbnail of Enveloping Algebras of Certain Types of Color Hom-Lie Algebras

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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Research paper thumbnail of On generalized Walsh bases

arXiv (Cornell University), Feb 28, 2018

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Research paper thumbnail of Non-degenerate Killing forms on Hom-Lie superalgebras

arXiv (Cornell University), Oct 5, 2020

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Research paper thumbnail of Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman color Hom-algebras

arXiv (Cornell University), May 7, 2022

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Research paper thumbnail of Enveloping algebras of color hom-Lie algebras

Turkish Journal of Mathematics, Jan 18, 2019

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Research paper thumbnail of Unital algebras of Hom-associative type and surjective or injective twistings

Journal of Generalized Lie Theory and Applications, 2009

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Research paper thumbnail of The Mathematics of Internet Search Engines

Acta Applicandae Mathematicae, Jul 16, 2008

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Research paper thumbnail of Averaging operators on <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>-deformed Witt and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>-deformed <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>W</mi><mo stretchy="false">(</mo><mn>2</mn><mo separator="true">,</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">W(2,2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mopen">(</span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mclose">)</span></span></span></span> algebras

arXiv (Cornell University), Apr 2, 2023

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Research paper thumbnail of Multiplicative n-Hom-Lie Color Algebras

Springer proceedings in mathematics & statistics, 2020

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Research paper thumbnail of Irreducible wavelet representations and ergodic automorphisms on solenoids

Operators and Matrices, 2011

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Research paper thumbnail of Hom-left-symmetric color dialgebras, Hom-tridendriform color algebras and Yau's twisting generalizations

arXiv (Cornell University), Dec 3, 2019

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Research paper thumbnail of On <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>λ</mi><mo separator="true">,</mo><mi>μ</mi><mo separator="true">,</mo><mi>γ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\lambda,\mu,\gamma)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">λ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">μ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span><span class="mclose">)</span></span></span></span>-derivations of BiHom-Lie algebras

arXiv (Cornell University), Oct 18, 2020

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Research paper thumbnail of Classification, centroids and derivations of two-dimensional Hom-Leibniz algebras

arXiv (Cornell University), Oct 25, 2021

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Research paper thumbnail of Constructions of BiHom-X algebras and bimodules of some BiHom-dialgebras

arXiv (Cornell University), May 4, 2021

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Research paper thumbnail of Matrix monotone functions on C*-algebras

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Research paper thumbnail of HNN-extension of involutive multiplicative Hom-Lie algebras

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Research paper thumbnail of A Note on Color Lie Algebras

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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Research paper thumbnail of New Paranormed Sequence Spaces l∞(p,λ) , c(p,λ) and c0(p,λ) Generated by an Infinite Matrix

International Journal of Mathematics Trends and Technology, Feb 25, 2014

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Research paper thumbnail of A new kind of two-parameter deformation of Heisenberg and parabose algebras and related deformed derivative

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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Research paper thumbnail of A Review on Hom-Gerstenhaber Algebras and Hom-Lie Algebroids

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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Research paper thumbnail of Enveloping Algebras of Certain Types of Color Hom-Lie Algebras

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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Research paper thumbnail of On generalized Walsh bases

arXiv (Cornell University), Feb 28, 2018

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Research paper thumbnail of Non-degenerate Killing forms on Hom-Lie superalgebras

arXiv (Cornell University), Oct 5, 2020

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Research paper thumbnail of Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman color Hom-algebras

arXiv (Cornell University), May 7, 2022

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Research paper thumbnail of Enveloping algebras of color hom-Lie algebras

Turkish Journal of Mathematics, Jan 18, 2019

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Research paper thumbnail of Unital algebras of Hom-associative type and surjective or injective twistings

Journal of Generalized Lie Theory and Applications, 2009

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Research paper thumbnail of The Mathematics of Internet Search Engines

Acta Applicandae Mathematicae, Jul 16, 2008

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Research paper thumbnail of Averaging operators on <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>-deformed Witt and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>-deformed <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>W</mi><mo stretchy="false">(</mo><mn>2</mn><mo separator="true">,</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">W(2,2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mopen">(</span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mclose">)</span></span></span></span> algebras

arXiv (Cornell University), Apr 2, 2023

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Research paper thumbnail of Multiplicative n-Hom-Lie Color Algebras

Springer proceedings in mathematics & statistics, 2020

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Research paper thumbnail of Irreducible wavelet representations and ergodic automorphisms on solenoids

Operators and Matrices, 2011

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Research paper thumbnail of Hom-left-symmetric color dialgebras, Hom-tridendriform color algebras and Yau's twisting generalizations

arXiv (Cornell University), Dec 3, 2019

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Research paper thumbnail of On <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>λ</mi><mo separator="true">,</mo><mi>μ</mi><mo separator="true">,</mo><mi>γ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\lambda,\mu,\gamma)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">λ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">μ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span><span class="mclose">)</span></span></span></span>-derivations of BiHom-Lie algebras

arXiv (Cornell University), Oct 18, 2020

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Research paper thumbnail of Classification, centroids and derivations of two-dimensional Hom-Leibniz algebras

arXiv (Cornell University), Oct 25, 2021

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