Representations and deformations of Hom-Lie-Yamaguti superalgebras

Let $(L,\alpha )$ 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 $(L,\alpha )$ and present some properties. Finally, we investigate the deformations of $(L,\alpha )$ by choosing some suitable cohomology.