On the Cohomology and Extensions of n‐ary Multiplicative Hom‐Nambu‐Lie Superalgebras

Lijun Tian, Baoling Guan and Yao Ma

Advances in Mathematical Physics, 2020, vol. 2020, issue 1

Abstract: In this paper, we discuss the representations of n‐ary multiplicative Hom‐Nambu‐Lie superalgebras as a generalization of the notion of representations for n‐ary multiplicative Hom‐Nambu‐Lie algebras. We also give the cohomology of an n‐ary multiplicative Hom‐Nambu‐Lie superalgebra and obtain a relation between extensions of an n‐ary multiplicative Hom‐Nambu‐Lie superalgebra b by an abelian one a and Z1b,a0¯. We also introduce the notion of T∗‐extensions of n‐ary multiplicative Hom‐Nambu‐Lie superalgebras and prove that every finite‐dimensional nilpotent metric n‐ary multiplicative Hom‐Nambu‐Lie superalgebra over an algebraically closed field of characteristic not 2 in the case α is a surjection is isometric to a suitable T∗‐extension.

Date: 2020
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https://doi.org/10.1155/2020/1961836

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:1961836

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