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

doi:10.1007/s10255-020-0982-8

CORC > 兰州理工大学 > 兰州理工大学

	The Skew-commutator Relations and Grobner-Shirshov Bases of Quantum Group of Type C-3
	Qiang, Cheng-xiu 2; Obul, Abdukadir 1
刊名	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
	2020-10-01
卷号	36 期号:4 页码:825-835
关键词	Ringel-Hall algebras root vectors indecomposable modules Grö bner-Shirshov bases compositions
ISSN号	0168-9673
DOI	10.1007/s10255-020-0982-8
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000602869700005
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/155077]
专题	兰州理工大学
作者单位	1.Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China 2.Lanzhou Univ Technol, Coll Elect & Informat Engn, Lanzhou 730050, Peoples R China;
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.