Representations and deformations of Hom-Lie-Yamaguti superalgebras

Abstract

Let (L, α) be a Hom-Lie-Yamaguti superalgebra. We first introduce the representation and cohomology theory of Hom-Lie-Yamaguti superalgebras. Furthermore, we introduce the notions of generalized derivations and representations of (L, α) and present some properties. Finally, we investigate the deformations of (L, α) by choosing some suitable cohomology.