Grobner-Shirshov Basis of Quantum Groups  

作　　者：Gulshadam Yunus Zhenzhen Gao Abdukadir Obul 

机构地区：[1]College of Mathematics and System Sciences, Xinjiang University Urumqi, Xinjiang 830046, China

出　　处：《Algebra Colloquium》2015年第3期495-516,共22页代数集刊（英文版）

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.

摘　　要：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.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.

关 键 词：Ringel-Hall algebra indecomposable modules Gr6bner-Shirshov basis skew-commutator relations 

分 类 号：O152.5[理学—数学] TU753[理学—基础数学]