In the talk, we first study the relationships between a Hom-Lie superalgebra and its induced 3-ary-Hom-Lie superalgebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived series, solvability, nilpotency, central extensions and cohomology.

We research Hom-Lie superalgebras. We  first give a sufficient and necessary condition of Hom-Lie superalgebras. We then revisit representations of Hom-Lie superalgebras, and show that there are a series of coboundary operators. We also introduce the notion of an omni-Hom-Lie superalgebra associated to a vector space and an even invertible linear map. We show that regular Hom-Lie superalgebra structures on a vector space can be characterized by Dirac structures in the corresponding omni-Hom-Lie superalgebra, and the underlying algebraic structure of the omni-Hom-Lie superalgebra is a Hom-Leibniz superalgebra.