Universal Central Extensions Of δ-Hom-Jordan Lie Algebras

In this paper,the structure of δ-Hom-Jordan Lie algebras is studied by using the universal central extension.The central extension and universal central extension of δ-Hom-Jordan Lie algebras and their semi-direct products are studied and discussed.Firstly,the definition of δ-Hom-Jordan Lie algebras is given,and some basic properties of δ-Hom-Jordan Lie algebras are given.Secondly,the Homaction between two δ-Hom-Jordan Lie algebras is defined,and the second-order homology space is given.In addition,by studying the universal central extension theory of δ-Hom-Jordan Lie algebras,it is found that the composition of the central extension of two δ-Hom-Jordan Lie algebras is no longer a central extension,and the definition of -central extension is introduced.Finally,we define the semi-direct products of two δ-Hom-Jordan Lie algebras,and construct the universal -central extensions of the semi-direct products.At the same time,we establish the relation between the universal -central extensions of the semi-direct products of two -perfect δ-Hom-Jordan Lie algebras and their universal -central extensions semi-direct products.