PBW Base Theorem For Universal Enveloping Algebras Of Differential Graded Poisson Algebras

Let R be a differential graded Poisson algebra whose underlying algebra structure is a graded commutative polynomial algebra,and I be a differential graded Poisson ideal of R.Set A:= R/I,then A is called a differential graded Poisson algebra given by generators and relations.In this thesis,we mainly study the theorem of the PBW basis for universal enveloping algebras of differential graded Poisson algebras given by generators and relations.More precisely,we give a "formula" for computing the universal enveloping algebra Ae of A.It is proved that the differential graded algebra Re has a PBW basis,and the PBW basis for a universal enveloping algebra Ae of A is given.Finally,as an application for the theorem of the PBW basis,we show that a differential graded symplectic ideal of a differential graded Poisson algebra A is the annihilator of a simple differential graded Poisson A-module.