The Structure Of Weak Hopf Module(CO)Algebras

The aim of this paper is not only to state the structure of weak Hopf module (co)algebras, but also provide a new kind of description of weak smash (co)products.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, the concept of weak Hopf module algebras is introduced, and its structure is studied if there exists a weak comodule algebra map φ:Hâ†'A for any weak H-Hopf module algebra A. Further, a new kind of description of weak smash product is given.In Chapter3, we study the structure of weak Hopf module coalgebras, and give its description.