基本典型李超代数的2-局部超导子

2-Local Superderivations on Basic Classical Lie Superalgebras

中文关键词:  基本典型李超代数  2-局部超导子  超导子

英文关键词:basic classical Lie superalgebras  2-local superderivation  superderivation

中文摘要:

      设$\mathbb{F}$是特征零代数闭域, $L$是域$\mathbb{F}$上除$A(n; n)$之外的基本典型李超代数. 本文证明了$L$上2-局部超导子是超导子，并且以spl(2; 2)的一个子代数为例说明存在2局部超导子不是超导子.

英文摘要:

      Let $\mathbb{F}$ be an algebraically closed field of characteristic zero, and $L$ be a basic classical Lie superalgebra except $A(n,n)$ over $\mathbb{F}$. In this paper, we prove that every 2-local superderivation on $L$ is a superderivation. Furthermore, we give an example to show that a subalgebra of $\mathrm{spl}(2,2)$ admits a 2-local superderivation which is not a superderivation.