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Keywords = n-LieDer pair

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17 pages, 290 KiB  
Article
Cohomologies of n-Lie Algebras with Derivations
by Qinxiu Sun and Zhixiang Wu
Mathematics 2021, 9(19), 2452; https://doi.org/10.3390/math9192452 - 2 Oct 2021
Cited by 10 | Viewed by 1999
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 [...] Read more.
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 (n1)-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. Full article
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