Representations and deformations of Hom-Lie-Yamaguti superalgebras

TL;DR

This paper develops the theory of representations, cohomology, derivations, and deformations for Hom-Lie-Yamaguti superalgebras, expanding the mathematical framework for these algebraic structures.

Contribution

It introduces the representation and cohomology theory for Hom-Lie-Yamaguti superalgebras, along with generalized derivations and deformation analysis.

Findings

Established a cohomology theory for Hom-Lie-Yamaguti superalgebras

Defined generalized derivations and studied their properties

Analyzed deformations using suitable cohomology groups

Abstract

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.