Cohomologies of <i>n</i>-Lie Algebras with Derivations

Abstract

The goal of this paper is to study cohomological theory of n-Lie algebras with derivations. We define the representation of an n-LieDer pair and consider its cohomology. Likewise, we verify that a cohomology of an n-LieDer pair could be derived from the cohomology of associated LeibDer pair. Furthermore, we discuss the (n−1)-order deformations and the Nijenhuis operator of n-LieDer pairs. The central extensions of n-LieDer pairs are also investigated in terms of the first cohomology groups with coefficients in the trivial representation.

Keywords

• <i>n</i>-Lie algebra
• representation
• <i>n</i>-LieDer pair
• cohomology
• deformation
• central extension