Some Related Studies On P-differential Graded Poisson Hopf Algebras

In this thesis,we study p-differential graded Poisson Hopf algebras.More precisely,the definition,examples and related properties of p-differential graded Poisson Hopf alge-bras are given.It is proved that the p-differential graded Poisson Hopf algebra is closed under the tensor product,and its category is a symmetric monoidal category.Finally,we show that the universal enveloping algebra of a p-differential graded Poisson bialgebra is a differential graded bialgebra,and give a counterexample to illustrate that the universal enveloping algebra of a p-differential graded Poisson Hopf algebra is not a differential graded Hopf algebra.