Cohomologies of n -Lie Algebras with Derivations

Qinxiu Sun and Zhixiang Wu
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Qinxiu Sun: Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China
Zhixiang Wu: School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

Mathematics, 2021, vol. 9, issue 19, 1-17

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: n -Lie algebra; representation; n -LieDer pair; cohomology; deformation; central extension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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