The Definition And Applications Of Universal Enveloping Algebras Of N-differential Graded Poisson Algebras

This thesis is a continuous work on universal enveloping algebras of differential graded Poisson algebras. The main results are made up of two chapters.In the first chapter, we mainly discuss the definition and some properties of universal enveloping algebras of n-differential graded Poisson algebras. More precisely, it is made up of three sections. In the first section, we give the definition of universal enveloping algebras of n-differential graded Poisson algebras. In the second section, we discuss some properties of universal enveloping algebras of n-differential graded Poisson algebras, that is, for any n-differential graded Poisson algebra A, we prove that A has a unique universal enveloping algebra Ae up to isomorphisms. In the third section, we prove that e is a covariant functor from the category of n-differential graded Poisson algebras to the category of differential graded algebras.In the second chapter, we mainly discuss the applications of universal enveloping algebras of n-differential graded Poisson algebras. More precisely, it is made up of two sections. In the first section, we prove that (Ae)op={Aop for any n-differential graded Poisson algebras A. In the second section, we prove that (A (?) B)e= Ae(?)Be, for any n-differential graded Poisson algebras A, B.