2-Local Superderivations on Basic Classical Lie Superalgebras

Abstract:

      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.