Universal Central Extensions Of Lie Supertriple Systems

Lie supertriple systems is the natural promotion of Lie algebras and Lie triple systems,and it is applied to solve the problem of Yang-Baxter equation.This paper first introduces the fundamental definition and relevant conceptions of Lie supertriple systems,which is considered to be the basis of the study of Lie supertriple systems issue.Then,the basic property and main results of the Lie supertriple systems were obtained;we also proved that the existence of the universal central extensions is if and only if the Lie supertriple systems are perfect;the existence of lifting of automorphisms and lifting of derivations of Lie supertriple systems are validated by the obtained result.