GK-维数有限的Hopf代数的分类

The main object of this project is to classify Hopf algebras of finite GK-dimension with mild conditions, particularly the Hopf algebras which need not be pointed or connected. Firstly, we complete the classification of semiprime regular noetherian Hopf algebras of GK-dimension 1. Secondly, we try to finish the classifications of pointed noetherian Hopf domains of GK-dimensions 2, 3 and 4. Furthermore, we study the structures and classifications of prime regular noetherian Hopf algebras of GK-dimensions 2, 3 and 4. Finally, based on the aforementioned results, we try to find some invatiants for classifying Hopf algebras of GK-dimension n>4.

本项目旨在分类比较一般的具有有限GK-维数的Hopf代数，尤其不再拘泥于点的或者连通的条件。首先，完成GK-维数为 1 的半素正则诺特Hopf代数的分类。其次，尝试完成 GK-维数为2、3、4的点的诺特Hopf整环的分类。进一步地，研究GK-维数为2、3、4的素正则诺特Hopf代数的结构和分类。最后，利用上述研究成果，我们试图找到一些不变量以分类GK-维数大于4的Hopf代数。