Hom-Bisuperalgebras And Double Extension Of Quasdratic Hom-Lie Superalgebras

In the first three sections of this paper,the definitions of Hom-bisuperalgebras are given by the Double superalgebras and even homomorphism. We provide several different ways for constructing Hom-double superalgebras by Double superalgebras and Hom-associative superalgebras etc.In section 4,we introduce Quadratic Hom-lie superalgebras.We provide a way for constructing a 2-cocycle on Quadratic Hom-lie superalgebras by extending the 2-cocycle on Quadratic lie superalgebras. We show the central extension of Hom-lie superalgebras.Then,We generalizes the notion of Double extension to Hom-lie superalgebras.