On ($\sigma,\tau$)-derivations of Lie superalgebras

Abstract

This paper is primarily devoted to studying ($\sigma,\tau$)-derivations of finite-dimensional Lie superalgebras over an algebraically closed field $\mathbb{F}$. We research some properties of ($\sigma,\tau$)-derivations and the relationship between the ($\sigma,\tau$)-derivations and other generalized derivations. Under certain conditions, a left-multiplication structure concerned with ($\sigma,\tau$)-derivations can induces a left-symmetric superalgebra structure. Let $L$ be a Lie superalgebra, we give a subgroup $G$ of $\mathrm{Aut}(L)$, research the interior of the $G$-derivations of $L$. Particularly, we calculate the corresponding Hilbert series when $G$ is a cyclic group.