Twisted Module Coalgebra And The Fundamental Structure Theorem Of Twisted Hopf Module

This paper mainly studies twisted relative Hopf modules induced by Harrison2-cocycles, and the fundamental structure theorem, as well as the structures of twisted dimodule coalgebras and twisted quntum Yang-Baxter module coalgebras. The paper is organized as follows:In chapter1, we introduce the background of this paper, the contents we studied and the main results.In chapter2, we introduce the definitions and some properties of Harrison2-cocycles. We introduce twisted comodule algebras and twisted relative Hopf modules, give some properties, and then present fundamental structure theorems of twisted relative Hopf modules.In chapter3, we introduce the twisted dimodule coalgebras and twisted quantum Yang-Baxter module coalgebras, and give some conclusions of smash coproducts and braided coproducts.