相关论文: On structures of BiHom-Superdialgebras and their d…
In this note, our goal is to describe the concept of generalized derivations in the context of BiHom-supertrialgebras. We provide a comprehensive analysis of the properties and applications of these generalized derivations, including their…
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 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…
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…
In this paper, we introduce the notion of BiHom-Lie conformal superalgebras. We develop its representation theory and define the cohomology group with coefficients in a module. Finally, we introduce conformal derivations of BiHom-Lie…
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…
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…
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…
This paper gives some constructions results and examples of BiHom-Poisson algebras. Next, BiHom-flexible algebras are defined and it is shown that admissible BiHom-Poisson algebras are BiHom-flexible. Furthermore, generalized derivations of…
The purpose of this paper is to study the structure and the algebraic varieties of BiHom-associative algebras. We provide a classication of n-dimensional BiHom-associative and BiHom-bialgebras and BiHom Hopf algebras for n $\le$ 3.
In this paper, we recall the notion of BiHom-generalization of Jordan superalgebras called BiHom-Jordan superalgebras in which, we investigate their representation and associated dual representation theory. We also introduce the notion of…
The goal of this paper is to study the structure of split regular BiHom-Leiniz superalgebras, which is a natural generalization of split regular Hom-Leiniz algebras and split regular BiHom-Lie superalgebras. By developing techniques of…
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…
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…
Throughout this paper, we will study Rota-Baxter operators and super O-operator of associative BiHom superalgebras, BiHom Lie superalgebras, BiHom pre-Lie superalgebras and BiHom-L-dendriform superalgebras. Then we give some properties of…
The purpose of this paper is to introduce Hom-prealternative superalgebras and their bimodules. Some constructions of Hom-prealternative superalgebras and Hom-alternative superalgebras are given, and their connection with Hom-alternative…
BiHom-Lie Colour algebra is a generalized Hom-Lie Colour algebra endowed with two commuting multiplicative linear maps. The main purpose of this paper is to define representations and a cohomology of BiHom-Lie colour algebras and to study…
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 split extension of BiHom- Lie algebra and construct the corresponding cohomology. Also, we establish a one-to-one correspondence between the equivalence classes of extensions of a BiHom-Lie algebra…
Hom-Lie superalgebras, which can be considered as a deformation of Lie superalgebras, are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. In this paper, we prove that there is only the trivial Hom-Lie superalgebra structure over a…