Local superderivations on Lie superalgebra $\mathfrak{q}(n)$

Czechoslovak Mathematical Journal

Haixian Chen, Ying Wang¹ 

关键词: simple Lie superalgebra;    superderivation;    local superderivation;   

DOI  :  10.21136/CMJ.2018.0597-16

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  Let $\mathfrak{q}(n)$ be a simple strange Lie superalgebra over the complex field $\mathbb{C}$. In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over $\mathbb{C}$ and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but $\mathfrak{p}(n)$ is an exception. In this paper, we introduce the definition of the local superderivation on $\mathfrak{q}(n)$, give the structures and properties of the local superderivations of $\mathfrak{q}(n)$, and prove that every local superderivation on $\mathfrak{q}(n)$, $n>3$, is a superderivation.

【 授权许可】

Unknown