BiHom-Lie superalgebra structures

Abstract

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 superalgebras from BiHom-associative superalgebras and Hom-Lie superalgebras by Yau's twist principle. Also, we explore some general classes of BiHom-Lie admissible superalgebras and describe all these classes via $G$-BiHom-associative superalgebras, where $G$ is a subgroup of the symmetric group $S_3$. Finally, we discuss the concept of ${\beta }^k$-derivation of BiHom-Lie superalgebras and prove that the set of all ${\beta }^k$-derivation has a natural BiHom-Lie superalgebra structure.

16 pages. arXiv admin note: text overlap with arXiv:1505.00469 by other authors

References in corpus (3)

• Deformations of Lie Algebras using $\sigma$-derivations
• Module Hom-algebras
• Hom-Lie superalgebra structures on finite-dimensional simple Lie superalgebras

Cited by in corpus (8)

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• BiHom-Lie colour algebras structures
• On split regular BiHom-Leibniz superalgebras
• Cohomology and linear deformation of BiHom-left-symmetric algebras
• On split regular BiHom-Poisson superalgebras
• The construction of 3-Bihom-Lie algebras
• BiHom-Poisson color algebras
• On BiHom-analogue of generalized Lie algebras