Sergei Silvestrov - Profile on Academia.edu (original) (raw)

Papers by Sergei Silvestrov

arXiv (Cornell University), May 4, 2021

The aim of this paper is to introduce and to give some constructions results of BiHom-X algebras ... more The aim of this paper is to introduce and to give some constructions results of BiHom-X algebras by using Yau's twisting, Rota Baxter and Some elements of centroids. Next, we define the bimodules of BiHom-left symmetric dialgebras, BiHomassociative dialgebras and BiHom-tridendriform algebras. A sequence of this kind of bimodules can be constructed. Their matched pairs are also introduced and related relevant properties are given.

Matrix monotone functions on C*-algebras

The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie ... more The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras, we provide an embedding theorem.

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.

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

In this paper we introduce a set of new paranormed sequence spaces (,) l p   , (,) c p  and 0 ... more In this paper we introduce a set of new paranormed sequence spaces (,) l p   , (,) c p  and 0 (,) c p  which are generated by an infinite lower uni triangular matrix n S   where () nk S s  is an infinite matrix given by, 1; 0 () 0; nk k n S s k n         as defined in [6]. We also compute the basis for the spaces (,) c p  and 0 (,) c p  , obtain β-dual for all these spaces and characterize the matrix classes  

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.

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.

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.

arXiv (Cornell University), Feb 28, 2018

This paper continues the study of orthonormal bases (ONB) of L 2 [0, 1] introduced in [DPS14] by ... more This paper continues the study of orthonormal bases (ONB) of L 2 [0, 1] introduced in [DPS14] by means of Cuntz algebra ON representations on L 2 [0, 1]. For N = 2, one obtains the classic Walsh system. We show that the ONB property holds precisely because the ON representations are irreducible. We prove an uncertainty principle related to these bases. As an application to discrete signal processing we find a fast generalized transform and compare this generalized transform with the classic one with respect to compression and sparse signal recovery. Contents 1. Introduction 1 2. The representation of the Cuntz algebra O N 3 3. Computations of generalized Walsh bases and of coefficients 5 4. A fast generalized Walsh transform 7 5. Uncertainty principles for Walsh transforms 8 6. Generalized Walsh vs. classic Walsh and DCT 13 References 17

arXiv (Cornell University), Oct 5, 2020

In this paper we investigate some important basic properties of simple Hom-Lie superalgebras and ... more In this paper we investigate some important basic properties of simple Hom-Lie superalgebras and show that a Hom-Lie superalgebra does not have any left or right nontrivial ideals. Moreover, we classify invariant bilinear forms on a given simple Hom-Lie superalgebra. Then we study the Killing forms on a Hom-Lie algebra which are examples of the invariant bilinear forms. Making use of the Killing forms, we find conditions for a Hom-Lie superalgebra to be classical. Furthermore, we check the conditions in which the Killing form of a Hom-Lie superalgebra is non-degenerate.

arXiv (Cornell University), May 7, 2022

The main feature of color Hom-algebras is that the identities defining the structures are twisted... more 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 is proved. Furthermore, we show that the class of admissible Hom-Novikov-Poisson color Hom-algebras is closed under tensor product.

Turkish Journal of Mathematics, Jan 18, 2019

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 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 Poincaré-Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.

Journal of Generalized Lie Theory and Applications, 2009

In this paper, we introduce a common generalizing framework for alternative types of Hom-associat... more In this paper, we introduce a common generalizing framework for alternative types of Hom-associative algebras. We show that the observation that unital Hom-associative algebras with surjective or injective twisting map are already associative has a generalization in this new framework. We also show by construction of a counterexample that another such generalization fails even in a very restricted particular case. Finally, we discuss an application of these observations by answering in the negative the question whether nonassociative algebras with unit such as the octonions may be twisted by the composition trick into Hom-associative algebras.

Acta Applicandae Mathematicae, Jul 16, 2008

This article presents a survey of techniques for ranking results in search engines, with emphasis... more This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.

arXiv (Cornell University), Apr 2, 2023

The aim of this paper is to give some constructions results of averaging operators on Hom-Lie alg... more The aim of this paper is to give some constructions results of averaging operators on Hom-Lie algebras. The homogeneous averaging operators on q-deformed Witt and q-deformed W (2, 2) Hom-algebras are classified. As applications, the induced Hom-Leibniz algebra structures are obtained and their multiplicativity conditions are also given.

Springer proceedings in mathematics & statistics, 2020

The purpose of this paper is to generalize some results on n-Lie algebras and n-Hom-Lie algebras ... more 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.

Irreducible wavelet representations and ergodic automorphisms on solenoids

Operators and Matrices, 2011

arXiv (Cornell University), Dec 3, 2019

The goal of this paper is to introduce and give some constructions and study properties of Hom-le... more 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 algebra, Hom-post-Lie color algebra and Hom-Poisson color dialgebras. Finally, we generalize Yau's twisting to a class of color Hom-algebras and used endomorphisms or elements of centroids to produce other color Hom-algebras from given one.

arXiv (Cornell University), Oct 18, 2020

In this paper, we generalize the results about generalized derivations of Lie algebras to the cas... more In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the classification of generalized derivations of Heisenberg BiHom-Lie algebras. The definition of the generalized derivation depends on some parameters (λ, µ, γ) ∈ C 3. In particular for (λ, µ, γ) = (1, 1, 1), we obtain classical concept of derivation of BiHom-Lie algebra and for (λ, µ, γ) = (1, 1, 0) we obtain the centroid of BiHom-Lie algebra. We give classifications of 2-dimensional BiHom-Lie algebra, centroides and derivations of 2-dimensional BiHom-Lie algebras.

arXiv (Cornell University), Oct 25, 2021

Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-L... more 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.

arXiv (Cornell University), May 4, 2021

The aim of this paper is to introduce and to give some constructions results of BiHom-X algebras ... more The aim of this paper is to introduce and to give some constructions results of BiHom-X algebras by using Yau's twisting, Rota Baxter and Some elements of centroids. Next, we define the bimodules of BiHom-left symmetric dialgebras, BiHomassociative dialgebras and BiHom-tridendriform algebras. A sequence of this kind of bimodules can be constructed. Their matched pairs are also introduced and related relevant properties are given.

Matrix monotone functions on C*-algebras

The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie ... more The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras, we provide an embedding theorem.

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.

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

In this paper we introduce a set of new paranormed sequence spaces (,) l p   , (,) c p  and 0 ... more In this paper we introduce a set of new paranormed sequence spaces (,) l p   , (,) c p  and 0 (,) c p  which are generated by an infinite lower uni triangular matrix n S   where () nk S s  is an infinite matrix given by, 1; 0 () 0; nk k n S s k n         as defined in [6]. We also compute the basis for the spaces (,) c p  and 0 (,) c p  , obtain β-dual for all these spaces and characterize the matrix classes  

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.

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.

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.

arXiv (Cornell University), Feb 28, 2018

This paper continues the study of orthonormal bases (ONB) of L 2 [0, 1] introduced in [DPS14] by ... more This paper continues the study of orthonormal bases (ONB) of L 2 [0, 1] introduced in [DPS14] by means of Cuntz algebra ON representations on L 2 [0, 1]. For N = 2, one obtains the classic Walsh system. We show that the ONB property holds precisely because the ON representations are irreducible. We prove an uncertainty principle related to these bases. As an application to discrete signal processing we find a fast generalized transform and compare this generalized transform with the classic one with respect to compression and sparse signal recovery. Contents 1. Introduction 1 2. The representation of the Cuntz algebra O N 3 3. Computations of generalized Walsh bases and of coefficients 5 4. A fast generalized Walsh transform 7 5. Uncertainty principles for Walsh transforms 8 6. Generalized Walsh vs. classic Walsh and DCT 13 References 17

arXiv (Cornell University), Oct 5, 2020

In this paper we investigate some important basic properties of simple Hom-Lie superalgebras and ... more In this paper we investigate some important basic properties of simple Hom-Lie superalgebras and show that a Hom-Lie superalgebra does not have any left or right nontrivial ideals. Moreover, we classify invariant bilinear forms on a given simple Hom-Lie superalgebra. Then we study the Killing forms on a Hom-Lie algebra which are examples of the invariant bilinear forms. Making use of the Killing forms, we find conditions for a Hom-Lie superalgebra to be classical. Furthermore, we check the conditions in which the Killing form of a Hom-Lie superalgebra is non-degenerate.

arXiv (Cornell University), May 7, 2022

The main feature of color Hom-algebras is that the identities defining the structures are twisted... more 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 is proved. Furthermore, we show that the class of admissible Hom-Novikov-Poisson color Hom-algebras is closed under tensor product.

Turkish Journal of Mathematics, Jan 18, 2019

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 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 Poincaré-Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.

Journal of Generalized Lie Theory and Applications, 2009

In this paper, we introduce a common generalizing framework for alternative types of Hom-associat... more In this paper, we introduce a common generalizing framework for alternative types of Hom-associative algebras. We show that the observation that unital Hom-associative algebras with surjective or injective twisting map are already associative has a generalization in this new framework. We also show by construction of a counterexample that another such generalization fails even in a very restricted particular case. Finally, we discuss an application of these observations by answering in the negative the question whether nonassociative algebras with unit such as the octonions may be twisted by the composition trick into Hom-associative algebras.

Acta Applicandae Mathematicae, Jul 16, 2008

This article presents a survey of techniques for ranking results in search engines, with emphasis... more This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.

arXiv (Cornell University), Apr 2, 2023

The aim of this paper is to give some constructions results of averaging operators on Hom-Lie alg... more The aim of this paper is to give some constructions results of averaging operators on Hom-Lie algebras. The homogeneous averaging operators on q-deformed Witt and q-deformed W (2, 2) Hom-algebras are classified. As applications, the induced Hom-Leibniz algebra structures are obtained and their multiplicativity conditions are also given.

Springer proceedings in mathematics & statistics, 2020

The purpose of this paper is to generalize some results on n-Lie algebras and n-Hom-Lie algebras ... more 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.

Irreducible wavelet representations and ergodic automorphisms on solenoids

Operators and Matrices, 2011

arXiv (Cornell University), Dec 3, 2019

The goal of this paper is to introduce and give some constructions and study properties of Hom-le... more 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 algebra, Hom-post-Lie color algebra and Hom-Poisson color dialgebras. Finally, we generalize Yau's twisting to a class of color Hom-algebras and used endomorphisms or elements of centroids to produce other color Hom-algebras from given one.

arXiv (Cornell University), Oct 18, 2020

In this paper, we generalize the results about generalized derivations of Lie algebras to the cas... more In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the classification of generalized derivations of Heisenberg BiHom-Lie algebras. The definition of the generalized derivation depends on some parameters (λ, µ, γ) ∈ C 3. In particular for (λ, µ, γ) = (1, 1, 1), we obtain classical concept of derivation of BiHom-Lie algebra and for (λ, µ, γ) = (1, 1, 0) we obtain the centroid of BiHom-Lie algebra. We give classifications of 2-dimensional BiHom-Lie algebra, centroides and derivations of 2-dimensional BiHom-Lie algebras.

arXiv (Cornell University), Oct 25, 2021

Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-L... more 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.