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Cohomologies of n -Lie Algebras with Derivations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Qinxiu Sun & Zhixiang Wu, 2021. "Cohomologies of n -Lie Algebras with Derivations," Mathematics, MDPI, vol. 9(19), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2452-:d:648853
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