Universal Central Extensions And Non-abelian Tensor Product Of Leibniz Conformal Algebras

In this paper,we study the universal central extension,the correspondence between crossed modules and cat~1-Leibniz conformal algebras,the non-abelian tensor product and the generalized conformal derivations of Leibniz conformal algebras.First,we give the concepts of conformal modules,conformal interactions,crossed modules and representations of Leibniz conformal algebras.After that,we give some definitions about the universal central extensions of Leibniz conformal algebras,discuss their properties and obtain some important results.Subsequently,by constructing the functor uce,we obtain the lifting of derivations and automorphism groups.Then the concepts of crossed module and cat~1-Leibniz conformal algebra of Leibniz con-formal algebra are given,and the isomorphism of crossed module of Leibniz conformal algebra is proved to correspond to the isomorphism class of cat~1-Leibniz conformal algebra one by one.Further,the non abelian tensor product is defined by means of the conformal action.