Hom-Lie Superalgebra Structures On Finite-Dimensional Classical Simple Lie Superalgebras

This paper is mainly to study Hom-Lie superalgebra structures on finite dimen-sional classical simple Lie superalgebras.Let g be a Lie superalgebra.A Hom-Lie su-peralgebra(g,[-,-],σ)consists of a Z2-graded vector space g,a bilinear map[-,-]and an even linear map σ.(g,σ)is called Hom-Lie superalgebra structures when(g,[-,-],σ)is Hom-Lie superalgebra.Hom-Lie superalgebras are Z2-graded general-ization of Hom-Lie algebras.And it can be considered as deformations of Lie superalge-bras.In[7]the authors did not state the centre of sl(m|n)0 and they used a conclusion in[12]which did not consider all about situation of go which include Sl2.This paper will further perfect it,and give Hom-Lie superalgebra structures on finite dimensional classical simple Lie superalgebras.