| 中文摘要 | 第4-6页 |
| Abstract | 第6-7页 |
| Table of Contents | 第8-10页 |
| Chapter 1 Introduction and preliminaries | 第10-24页 |
| 1.1 Hopf algebras and their modules | 第11-18页 |
| 1.2 The almost split sequences | 第18-22页 |
| 1.3 Corings and their comodules | 第22-24页 |
| Chapter 2 The representations of quantum double of dihedral groups | 第24-42页 |
| 2.1 Induced module and Yetter-Drinfeld kG-module | 第25-28页 |
| 2.2 The indecomposable representations of some finite groups | 第28-38页 |
| 2.3 The indecomposable representations of D(kD_n) | 第38-42页 |
| Chapter 3 Almost split sequences for quantum double of finite groups | 第42-54页 |
| 3.1 Almost split sequences for quantum double of finite groups | 第42-45页 |
| 3.2 Application to the quantum double of dihedral groups | 第45-54页 |
| 3.2.1 Almost split sequences for group algebra kD_n | 第46-49页 |
| 3.2.2 Almost split sequence for group algebra kC_n | 第49-54页 |
| Chapter 4 Grothendieck group of quantum double of dihedral groups | 第54-78页 |
| 4.1 The Grothendieck group of finite groups | 第54-60页 |
| 4.2 The Grothendieck group of D(kD_n) | 第60-69页 |
| 4.3 Further description of G_0(D(kD_n)) | 第69-72页 |
| 4.4 Appendix: The case n =6 and p=3 | 第72-78页 |
| Chapter 5 A class of standard bases of polynomial algebras and its applications | 第78-92页 |
| 5.1 Standard bases of polynomial algebras | 第79-83页 |
| 5.2 Two combinatorial formulae | 第83-87页 |
| 5.3 Clebsch-Gordan formula | 第87-92页 |
| Chapter 6 Equivalence between categories of modules and categories of comodules | 第92-102页 |
| 6.1 (C,A)-injective comodules | 第93-96页 |
| 6.2 Equivalences between categories | 第96-102页 |
| Bibliography | 第102-106页 |
| Publications | 第106-107页 |
| Acknowledgements | 第107-108页 |
