The Skew-commutator Relations and Grobner-Shirshov Bases of Quantum Group of Type c3  

作　　者：Cheng-xiu QIANG Abdukadir OBUL 

机构地区：[1]College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China [2]College of Mathematics and System Science,Xinjiang University,Urumqi 830046,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第4期825-835,共11页应用数学学报（英文版）

基　　金：This paper is supported by the National Natural Science Foundation of China(No.11061033).

摘　　要：In this paper,we give a Grobner-Shirshov basis of quantum group of type C3 by using the Ringel-Hall algebra approach.For this,first we compute all skew-commutator relations between the isoclasses of indecomposable reprersentations of Ringel-Hall algebras of type C3 by using an“inductive”method.Precisely,we do not use the traditional way of computing the skew-commutative relations,that is first compute all Hall polynomials then compute the corresponding skew-commutator relations;contrarily,we compute the“easier”skew-commutator relations which corresponding to those exact sequences with middile term indecomposable or the split exact sequences first,then“inductive”others from these“easier”ones and this in turn gives Hall polynomials as a byproduct.Then we prove that the set of these relations is closed under composition.So they constitutes a minimal Grobner-Shirshov basis of the positive part of quantum group of type C3.Dually,we get a Grobner-Shirshov basis of the negative part of quantum group of type C3.And finally we give a Grobner-Shirshov basis for the whole quantum group of type C3.

关 键 词：Ringel-Hall algebras root vectors indecomposable modules Grobner-Shirshov bases COMPOSITIONS 

分 类 号：O152.5[理学—数学]