In this paper, by using the Ringel-Hall algebra method, we prove that the set of the skew-commutator relations of quantum root vectors forms a minimal GrSbner- Shirshov basis for the quantum groups of Dynkin type. As ...In this paper, by using the Ringel-Hall algebra method, we prove that the set of the skew-commutator relations of quantum root vectors forms a minimal GrSbner- Shirshov basis for the quantum groups of Dynkin type. As an application, we give an explicit basis for the types E7 and Dn.展开更多
基金Supported by the National Natural Science Foundation of China （11061033）.Acknowledgements. Part of this work is done during the corresponding author＇s visiting the Stuttgart University with the support of China Scholarship Council. With this opportunity, he expresses his gratefulness to Professor Steffen Koenig and the Institute of Algebra and Number Theory of Stuttgart University and the China Scholarship Council.
文摘In this paper, by using the Ringel-Hall algebra method, we prove that the set of the skew-commutator relations of quantum root vectors forms a minimal GrSbner- Shirshov basis for the quantum groups of Dynkin type. As an application, we give an explicit basis for the types E7 and Dn.
