Maschke Type Theorems For Partial Smash Products And Structure Theorem For Coquasi-Hopf Bicomodules

This paper mainly studies two aspects:first, we give the Maschke type theorem for L-R smash products and partial smash products; second, we give the structure theorem for coquasi-Hopf bicomodules and as its application we get the structure theorem for coquasi-Hopf module coalgebras.This paper is organized as follows:In Chapter1, we introduce the recent development of L-R smash products, partial Hopf action and coquasi-Hopf algebras. And the main results studied in this paper will be given. We also recall some concepts and definitions used in this paper.In Chapter2, we first show the Maschke type theorem for L-R smash products via an algebra isomorphism between L-R smash products and smash products. Then, using the way of Ref [20], we get the Maschke type theorem for partial smash products.In Chapter3, we will show that for a coquasi-Hopf bicomodule N and its quotient space N, there is an isomorphism between N and N(?)H as coquasi-Hopf bicomodules. And we use it to describe the structure theorem for coquasi-Hopf module coalgebras.