The Skew-commutator Relations and Grobner-Shirshov Bases of Quantum Group of Type C-3

doi:10.1007/s10255-020-0982-8

	The Skew-commutator Relations and Grobner-Shirshov Bases of Quantum Group of Type C-3
	Qiang, Cheng-xiu 1; Obul, Abdukadir 2
	2020-10
发表期刊	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
卷号	36 期号:4 页码:825-835
摘要	In this paper, we give a Grobner-Shirshov basis of quantum group of type DOUBLE-STRUCK CAPITAL C-3 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 DOUBLE-STRUCK CAPITAL C-3 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 DOUBLE-STRUCK CAPITAL C-3. Dually, we get a Grobner-Shirshov basis of the negative part of quantum group of type C-3. And finally we give a Grobner-Shirshov basis for the whole quantum group of type DOUBLE-STRUCK CAPITAL C-3.
关键词	Ringel-Hall algebras root vectors indecomposable modules Grö bner-Shirshov bases compositions
DOI	10.1007/s10255-020-0982-8
收录类别	SCIE
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000602869700005
出版者	SPRINGER HEIDELBERG
来源库	WOS
引用统计	被引频次[WOS]：0 [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://ir.lut.edu.cn/handle/2XXMBERH/155077
专题	兰州理工大学
通讯作者	Qiang, Cheng-xiu
作者单位	1.Lanzhou Univ Technol, Coll Elect & Informat Engn, Lanzhou 730050, Peoples R China; 2.Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
第一作者单位	电气工程与信息工程学院
通讯作者单位	电气工程与信息工程学院
第一作者的第一单位	电气工程与信息工程学院
推荐引用方式 GB/T 7714	Qiang, Cheng-xiu,Obul, Abdukadir. The Skew-commutator Relations and Grobner-Shirshov Bases of Quantum Group of Type C-3[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2020,36(4):825-835.
APA	Qiang, Cheng-xiu,&Obul, Abdukadir.(2020).The Skew-commutator Relations and Grobner-Shirshov Bases of Quantum Group of Type C-3.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,36(4),825-835.
MLA	Qiang, Cheng-xiu,et al."The Skew-commutator Relations and Grobner-Shirshov Bases of Quantum Group of Type C-3".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 36.4(2020):825-835.