Structures Of Hom-Superalgebras

In this paper, we mainly consider structures of Horn-associative superalgebras, Hom-Malcev superalgebras and Hom-Lie2-superalgebras.In the first chapter, we introduce the background and significance.In chapter2, we define the representation and bimodule of Hom-associative superalgebras, and give the cohomology group by using the representation and bimodule. Moreover, we obtain conditions for the vanishing of cohomology group in terms of the action of enveloping algebras on the bimodule.In chapter3, Hom-Malcev superalgebras can be considered as a deformation of Malcev superalgebras. First, we give the definition of Hom-Malcev superalgebras. Secondly, we char-acterize the operator and representation of Hom-Malcev superalgebras. Finally, we study the central extension and double extension of quadratic Hom-Malcev superalgebras.In chapter4, we study Hom-Lie2-superalgebras. First, we give the definition of Hom-Lie2-superalgebras, which is the categorification and deformation of Lie superalgebras. Secondly, we study the derivation of Hom-Lie2-superalgebras and some properties. Thirdly, we obtain the deformation, representation and abelian extensions related to the2-cocycle and Nijenhuis operators. Finally, we construct the strict and skeletal Hom-Lie2-superalgebras by means of Hom-associative Rota-Baxter superalgebras respectively.