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
In this paper, by using PBW bases for the twisted generic composition algebras of affine type, we prove that the set of the skew-commutator relations of the iso-classes of indecomposable representations forms a minima...In this paper, by using PBW bases for the twisted generic composition algebras of affine type, we prove that the set of the skew-commutator relations of the iso-classes of indecomposable representations forms a minimal GrSbner-Shirshov basis for the twisted generic composition algebras of affine type.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.
基金Supported by National Science Foundation of China （Grant No. 11061033, 11361056）.
文摘In this paper, by using PBW bases for the twisted generic composition algebras of affine type, we prove that the set of the skew-commutator relations of the iso-classes of indecomposable representations forms a minimal GrSbner-Shirshov basis for the twisted generic composition algebras of affine type.
