Double Derivations of n-Lie Superalgebras

Author:

Sun Bing1,Chen Liangyun1,Zhou Xin12

Affiliation:

1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

2. School of Mathematical and Statistics, Yili Normal University, Yining, Xinjiang 835000, China

Abstract

Let 𝔤 be an n-Lie superalgebra. We study the double derivation algebra [Formula: see text] and describe the relation between [Formula: see text] and the usual derivation Lie superalgebra Der(𝔤). We show that the set [Formula: see text] of all double derivations is a subalgebra of the general linear Lie superalgebra gl(𝔤) and the inner derivation algebra ad(𝔤) is an ideal of [Formula: see text]. We also show that if 𝔤 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(𝔤) in [Formula: see text] is trivial. Finally, we give that for every perfect n-Lie superalgebra 𝔤, the triple derivations of the derivation algebra Der(𝔤) are exactly the derivations of Der(𝔤).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The Schur multiplier of an n-Lie superalgebra;Communications in Algebra;2022-01-12

2. n-derivations of lie color algebras;Filomat;2021

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