| Acknowledgements | 第1-4页 |
| Abstract in Chinese | 第4-5页 |
| Abstract | 第5-8页 |
| 1 Introduction | 第8-17页 |
| ·Background | 第8-11页 |
| ·Main results | 第11-15页 |
| ·Organization | 第15-17页 |
| 2 Preliminaries | 第17-27页 |
| ·Cellular algebras | 第17-23页 |
| ·Quasi-hereditary algebras and standardly stratified algebras | 第23-27页 |
| 3 Quasi-heredity and semi-simplicity of cellular algebras | 第27-47页 |
| ·Quasi-heredity characterized by Ext~1 | 第27-35页 |
| ·Quasi-heredity characterized by Ext~2 | 第35-43页 |
| ·Semi-simplicity of cellular algebras | 第43-47页 |
| 4 Cartan determinants of cellular algebras | 第47-58页 |
| ·Cartan determinants | 第48-54页 |
| ·Cellular algebras with Cartan determinant two | 第54-58页 |
| 5 Projective-injective modules over cellular algebras | 第58-66页 |
| ·Main theorem and motivating examples | 第58-61页 |
| ·Proof of the theorem | 第61-66页 |
| 6 A new class of cellular algebras — cyclotomic blob algebras | 第66-87页 |
| ·Category of m-decoratcd tangles | 第67-71页 |
| ·Cyclotomic blob algebras and their cellular structure | 第71-78页 |
| ·Irreducible representations and quasi-heredity | 第78-81页 |
| ·Restriction of the cell modules | 第81-87页 |
| 7 References | 第87-93页 |
| Appendix A. Publications while studying in the doctoral program | 第93-94页 |
| Appendix B. Summary in Chinese | 第94-117页 |
