Generalized Derivations of Hom-Lie Superalgebras

Abstract

In this paper, we give some basic properties of the generalized derivation algebra $\mathrm{GDer}(L)$ of a Hom-Lie superalgebra $L$. In particular, we prove that $\mathrm{GDer}(L)=\mathrm{QDer}(L)+\mathrm{QC}(L)$, the sum of the quasiderivation algebra and the quasicentroid. We also prove that $\mathrm{QDer}(L)$ can be embedded as derivations in a larger Hom-Lie superalgebra.

13pages