Finite-dimensional Simple Poisson Modules Over Two Poisson Algebras

In this thesis,we study finite-dimensional simple Poisson modules over two Poisson algebras.More precisely,according to the different algebras T,the Poisson algebras A:=T/(t-1)T can be constructed and Poisson maximal ideals of A are given.Then all finite-dimensional simple Poisson modules over A can be classified.Finally,we extend the results of finite-dimensional simple Poisson modules over certain Poisson algebras to universal enveloping algebras.