Universal Central Extensions Of δ-Hom-Jordan Lie Superalgebras

This paper give the property and definition of δ-Hom-Jordan Lie superalgebras.Further definition the Hom-action between two δ-Hom-Jordan Lie superalgebras.Then we use low dimensional chain complex and give the lower order homology space.Sencondly,we study the composition of the central extension of two δ-Jordan Lie superalgebras and vertify the composition of them is universal α-central extension.We define the α-central extension and the universal α-central extension.The sufficient and necessary conditions are obtained forδ-Hom-Jordan Lie superalgebras to have the universal central extension structure.Then,the properties and definitions of functors are given.We define the semi-direct products of two δ-Hom-Jordan Lie superalgebras.Constructing the universal α-central extensions of the semi-direct products.Finally,to analyze the relationship between the universal α-central extensions of the semi-direct products and the semi-direct products of universal α-central extensions for twoα-perfect δ-Hom-Jordan Lie superalgebras.