BiHom-Lie superalgebra structures

2016/10/07 by Wang, Shengxiang, Guo, Shuangjian
#17B05 #17B40 #17B70 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1610.02290

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 S₃. Finally, we discuss the concept of β^k-derivation of BiHom-Lie superalgebras and prove that the set of all β^k-derivation has a natural BiHom-Lie superalgebra structure.

Related

• BiHom pre-Lie Superalgebras and Related Structures
• Cohomology and conformal derivations of BiHom-Lie conformal superalgebras
• Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras
• Superalgebras with Homogeneous structures of Lie type
• Generalized derivations of BiHom-supertrialgebras