Ore Extension And The Indecomposable U_q(osp(1,2,c))-modules

The theory of the representatiOns of quantum superalgebras is a new branch of mathmatics.Nowadays only few conclusions have been drawn in the indecomposable modules of quantum superalgebras. So this thesis focus on the classification of the indecomposable modules of quantum superalgebras Uq(osp(1,2,c))by Ore extension.Let A be a subalgebra of Uq(osp(1,2,c))generated by K,K-1,c,c-1,F.α be a isomorphism of A and6be a α-derivation of A. Setting A6=ker6. If q is not a root of unity,A6is a subalgebra generated by K,K-1,c,c-1.If q is a primitive d-th root of unity,Aδ is a subalgebra generated by K,K-1,c,c-1,Fe.Given a finite dimensional Aδ-module M,then A(?)Aδ M is a Uq (osp(1,2,c))-module in a natural way. Assume that M is finite dimension indecomposable Aδ-module,we prove that A(?)Aδ M is an indecomposable Uq(osp(1,2,c))-module and describe the submodules structure of A(?)AδM.Assume that M is an indecomposable Aδ-module satisfying some conditions.Let {m1,m2,…,ms}be a basis of M,Mi:=span{m1,m2,…,mi}.If q is not a root of unity,then C[x](?)M is a Uq(osp(1,2,c))-module in a natural way.Ni:=span{xj(?)mi|j≥n+1),i=1,2,…,s.Then(1)If λ≠±qnα for any n∈Z,then C[x](?)Mi(1≤i≤s) qre all non-zero sub-modules of C[x](?)M.(2)If λ=±qnα for some n∈Z,then C[x](?)Mi and C[x](?)Mi-1(?)Ni-(1≤i≤s) are all non-zero submodules of C[x](?)M.If q is a primitive d-th root of unity,then Ce[x](?)M is a Uq(osp(1,2,c))-module in a natural way,and Ce[x]is a vector space generated by1,x,…,xe-1. Ni:=span {xj(?)mi|n+1≤j≤e-1},i=1,2,…,s.Then(1)If λ≠±qnα,0≤n≤e-2,then Ce[x](?)Mi(1≤i≤s)are all non-zero sub-modules of Ce[x](?)M.(2)If λ≠±qnα,0≤n≤e-2,then Ce[x](?)Mi and Ce[x](?)Mi-1(?)Ni(1≤i≤s) are all non-zero submodules of Ce[x](?)M.