Grobner-Shirshov Basis of Quantum Groups

作     者：Gulshadam Yunus Zhenzhen Gao Abdukadir Obul 

作者机构：College of Mathematics and System Sciences Xinjiang University Urumqi Xinjiang 830046 China 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2015年第22卷第3期

页      面：495-516页

核心收录：

学科分类：07[理学] 081401[工学-岩土工程] 08[工学] 070104[理学-应用数学] 0814[工学-土木工程] 0701[理学-数学] 

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 

主　　题：Ringel-Hall algebra indecomposable modules Gr6bner-Shirshov basis skew-commutator relations 

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.