The Structure Theorem Of Graded Weak Doi-Hopf Modules

In this paper, we introduce the coinvariant subspace of a weak Doi-Hopf module associated group-like elements, and basing on the weak Doi-Hopf module structure theorem, give the fundamental structure theorem of graded weak Doi-Hopf modules associated group-like elements and its applications.The paper is organized as follows:In chapter1, we introduce the recent development of weak Hopf algebras, and also give the background of this paper. Then the main results studied in this paper are given.In chapter2, we give the fundamental structure theorem of graded weak Doi-Hopf modules associated group-like elements. Consequently, we give some applications of the theorem by using the structure theorem.In chapter3, we give the fundamental structure theorem of graded weak comudule algebras on base of the fundamental structure theorem of graded weak Doi-Hopf modules.In chapter4, We gain a Maschke theorem for weak comodule algebras.