New Simple (?)-modules From Wely Algebra Modules

Let P be an admissible Wd-module and V a(?)-module,we can define a Wd-module F(P,V)=P(?)V,called Shen-Larsson's module.Since Wd contains a natural subalgebra isomorphic to we can regard F(P,V)as an(?)-module.The structure of F(P,V)was well studied by many mathematicians both as a Wd-module and as an(?)-module.In this thesis,using similar ideas as above,we construct a class of modules for the affine Lie algebra(?)also denoted by F(P,V).Then we investigate these modules in details for the case d=1.More precisely,we construct the(?)-module F(P,V)from a module P over the degree-2 Weyl algebra K2 and a module V over the 2-dimensional solvable Lie algebra b.We obtain the irreducibility and study the submodule structure in the reducible case,according to whether the dimension of V is finite or not.Then we determine the isomorphisms for such(?)-modules.To illustrate our results,we also present some examples using Bavula's construction of modules for generalized Weyl algebras.