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Related papers: BiHom-Lie superalgebra structures

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The paper concerns the cohomology of (multiplicative) BiHom-associative trialgebras. We first detail the correspondence between central extensions and second cohomology. This is followed by a general cohomology theory that unifies those of…

Rings and Algebras · Mathematics 2024-04-25 Erik Mainellis , Bouzid Mosbahi , Ahmed Zahari

The aim of this paper is to introduce and study BiHom-associative dialgebras. We give various constructions and study its connections with BiHom-Poisson dialgebras and BiHom-Leibniz algebras. Next we discuss the central extensions of…

Rings and Algebras · Mathematics 2021-01-20 Ahmed Zahary , Ibrahima Bakayoko

In this paper, first we show that there is a Hom-Lie algebra structure on the set of $(\sigma,\sigma)$-derivations of a commutative algebra. Then we construct dual representations of a representation of a Hom-Lie algebra. We introduce the…

Rings and Algebras · Mathematics 2018-08-27 Liqiang Cai , Yunhe Sheng

This paper defines compatible BiHom-Lie algebras by twisting the compatible Lie algebras by two linear commuting maps. We show the characterization of compatible BiHom-Lie algebra as a Maurer-Cartan element in a suitable bidifferential…

Rings and Algebras · Mathematics 2023-03-24 Asif Sania , Basdouri Imed , Bouzid Mosbahi , Nacib Saber

In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…

Rings and Algebras · Mathematics 2023-08-01 Shuangjian Guo , Ripan Saha

Hom-Lie algebras are generalizations of Lie algebras that arise naturally in the study of nonassociative algebraic structures. In this paper, the concepts of solvable and nilpotent Hom-Lie algebras studied further. In the theory of groups,…

Rings and Algebras · Mathematics 2023-05-02 Shadi Shaqaqha , Nadeen Kdaisat

The purpose of this paper is to introduce and study the notion of BiHom-pre-alternative algebra which may be viewed as a BiHom-alternative algebra whose product can be decomposed into two compatible pieces. Furthermore, we introduce the…

Rings and Algebras · Mathematics 2019-03-20 Tewfik Chtioui , Sami Mabrouk , Abdenacer Makhlouf

Bihom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps. In this paper, we study cohomology and representations of Bihom-Lie algebras. In particular, derivations, central extensions,…

Representation Theory · Mathematics 2016-10-17 Yongsheng Cheng , Huange Qi

In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory of Hom-Lie conformal superalgebras and discuss some…

Rings and Algebras · Mathematics 2018-07-11 Shuangjian Guo , Lihong Dong , Shengxiang Wang

The aim of this paper is to introduce the notion of restricted Hom- Lie superalgebras. This class of algebras is a generalization of both restricted Hom-Lie algebras and restricted Lie superalgebras. In this paper, we present a way to…

Rings and Algebras · Mathematics 2022-11-02 Shadi Shaqaqha

The purpose of this paper is to define the representation and the cohomology of Hom-Lie superalgebras. Moreover we study Central extensions and provide as application the computations of the derivations and second cohomology group of…

Rings and Algebras · Mathematics 2012-04-30 Faouzi Ammar , Abdenacer Makhlouf , Nejib Saadoui

A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov and extended by Larsson and Silvestrov to…

Rings and Algebras · Mathematics 2007-06-13 A. Makhlouf , S. Silvestrov

The aim of this paper is to give some construction results and examples of BiHom-alternative and BiHom-Jordan algebras. Next, we define BiHom-alternative and BiHom-Jordan (bi)modules and we prove that from a given BiHom-alternative and…

Rings and Algebras · Mathematics 2020-08-18 Sylvain Attan , Ismail Laraiedh

The aim of this paper is to generalise the construction of $3$-Bihom-Lie superalgebras and we provide some properties can be lifted to its $T^{\ast}$-extensions such as nilpotency, solvability and decomposition. We study the…

Rings and Algebras · Mathematics 2020-04-21 Ismail Laraiedh

We introduce the new concept of braided Hom-Lie bialgebras which is a generalization of Sommerh\"{a}user-Majid's braided Lie bialgebras and Yau's Hom-Lie bialgebras. Using this concept we give the unified product construction for Hom-Lie…

Quantum Algebra · Mathematics 2022-03-15 Tao Zhang

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and…

Rings and Algebras · Mathematics 2017-11-23 Jun Zhao , Lamei Yuan , Liangyun Chen

First, we construct some families of nonsolvable anticommutative algebras, solvable Lie algebras and even nilpotent Lie algebras, that can be endowed with the structure of a simple Hom-Lie algebra. This situation shows that a classification…

Rings and Algebras · Mathematics 2022-05-23 Youness El Kharraf

In this paper we introduce the notion of Hom-pre-Lie bialgebra in the general framework of the cohomology theory for Hom-Lie algebras. We show that Hom-pre-Lie bialgebras, standard Manin triples for Hom-pre-Lie algebras and certain matched…

Rings and Algebras · Mathematics 2020-01-01 Shanshan Liu , Abdenacer Makhlouf , Lina Song

We investigate generalized derivations of $n$-BiHom-Lie algebras. We introduce and study properties of derivations, $( \alpha^{s},\beta^{r}) $-derivations and generalized derivations. We also study quasiderivations of $n$-BiHom-Lie…

Rings and Algebras · Mathematics 2020-04-03 Amine Ben Abdeljelil , Mohamed Elhamdadi , Ivan Kaygorodov , Abdenacer Makhlouf

In this paper some characterizations of Hom-Leibniz superalgebras are given and some of their basic properties are found. These properties can be seen as a generalization of corresponding well-known properties of Hom-Leibniz algebras.…

Rings and Algebras · Mathematics 2018-05-15 Donatien Gaparayi , Sylvain Attan , A. Nourou Issa