相关论文: Classification of 3-Dimensional BiHom-Associative …
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…
Due to the immense importance of BiHom Type algebras and cohomology of various algebraic structures, this paper is devoted to defining the BiHom-associative dialgebra, its derivation, generalized derivation, and quasi-derivation. We…
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…
The basic objective of this research work is to investigate the stucture of BiHom-associative trialgebras.\,In this respect we build up one important class of BiHom-trialgebras and determine properties of right, left and middle operations…
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…
A BiHom-associative algebra is a (nonassociative) algebra $A$ endowed with two commuting multiplicative linear maps $\alpha,\beta\colon A\rightarrow A$ such that $\alpha (a)(bc)=(ab)\beta (c)$, for all $a, b, c\in A$. This concept arose in…
The aim of this paper is to introduce $n$-ary BiHom-algebras, generalizing BiHom-algebras. We introduce an alternative concept of BiHom-Lie algebra called BiHom-Lie-Leibniz algebra and study various type of $n$-ary BiHom-Lie algebras and…
In this paper, we introduce the notion of a BiHom-Lie conformal algebra and develop its cohomology theory. Also, we discuss some applications to the study of deformations of regular BiHom-Lie conformal algebras. Finally, we introduce…
BiHom-superdialgebras are clear generalization of Hom-superdialgebras. The purpose of this note is to describe and to survey structures of BiHom-superdialgebras. Then we derive derivations of BiHomsuperdialgebras.
In this paper, we classify flnite dimensional multiplicative simple BiHom-Lie algebras by investigating the corresponding semisimple Lie algebras and we give a complete classification of the complex 3-dimensional multiplicative BiHom-Lie…
The aim of this paper is to introduce and study BiHom-Poisson algebras, in particular Non-BiHom-Commutative BiHom-Poisson algebras. We discuss their representation theory and Semi-direct product. Furthermore, we characterize admissible…
In this paper, we introduce the definition of generalized BiHom-Lie algebras and generalized BiHom-Lie admissible algebras in the category ${}_H{\mathcal M}$ of left modules for any quasitriangular Hopf algebra $(H, R) $. Also, we describe…
The purpose of this paper is to investigate finite-dimensional superbialgebras and Hopf superalgebras. We study connected superbialgebras and provide a classification of non-trivial superbialgebras and Hopf superalgebras in dimension $n$…
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…
The aim of this paper is to deal with BiHom-alternative algebras which are a generalization of alternative and Hom-alternative algebras, their structure is defined with two commuting multiplicative linear maps. We study cohomology and…
BiHom-Akivis algebras are introduced. The BiHom-commutator-BiHom-associator algebra of a regular BiHom-algebra is a BiHom-Akivis algebra. It is shown that BiHom-Akivis algebras can be obtained from Akivis algebras by twisting along two…
The aim of this paper is introduce and give some constructions results and examples of n-BiHom-Lie color algebras. Next, we introduce the definition of BiHom-modules over n- BiHom-Lie color algebras and we provide some properties. Moreover…
The purpose of this paper is to study the construction of $3$-Bihom-Lie algebras. We give some ways of constructing $3$-Bihom-Lie algebras from $3$-Bihom-Lie algebras and $3$-totally Bihom-associative algebras. Furthermore, we introduce…
The aim of this paper is to introduce the notion of BiHom-Lie superalgebras. This class of algebras is a generalization of both BiHom-Lie algebras and Hom-Lie superalgebras. In this article, we first present two ways to construct BiHom-Lie…
Bihom-associative algebras have been recently introduced in the study of group hom-categories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain…