量子群U_q(C_3)及其不可约模的Grbner-Shirshov基

Grbner-Shirshov Basis of Quantum Group U_q(C_3) and Its Irreducible Modules

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摘要为了研究量子群U_q(C_3)及其有限维不可约模的Grbner-Shirshov基,基于赋值图C3的Auslander-Reiten理论和表示的Grbner-Shirshov基理论,运用Ringel-Hall代数方法,构造了量子群U_q(C_3)的Grbner-Shirshov基,进而用双自由模及钻石-合成引理,给出量子群U_q(C_3)的有限维不可约模的Grbner-Shirshov基. Based on Auslander-Reiten theory of valued graph C3 and Gr?bner-Shirshov bases for representation theory, First by using the Ringel-Hall algebra approach, a Gr?bner-Shirshov basis of quantum group Uq ( C3 ) was constructed. Then, a Gr?bner-Shirshov basis of finite dimensional irreducible modules of Uq ( C3 ) was given by using double free module and composition lemma.

作者高珍珍杨士林阿布都卡的·吾甫

机构地区北京工业大学应用数理学院新疆大学数学与系统科学学院

出处《北京工业大学学报》 CAS CSCD 北大核心 2016年第4期632-636,共5页 Journal of Beijing University of Technology

基金国家自然科学基金资助项目(11471186)

关键词量子群 Gr6bner-Shirshov基双自由模 quantum group Grbner-Shirshov basis double free modules

分类号 O152 [理学—基础数学]

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共引文献5

1Chengxiu QIANG Abdukadir OBUL.Skew-commutator relations and Grobner- Shirshov basis of quantum group of type F4[J].Frontiers of Mathematics in China,2014,9(1):135-150. 被引量：5
2缪玥,阿布都卡的.吾甫.D_4型量子包络代数的Gelfand-Kirillov维数（英文）[J].数学杂志,2015,35(6):1329-1340.
3Ghani USTA,Abdukadir OBUL.Grbner-Shirshov Bases of Irreducible Modules of the Quantum Group of Type G_2[J].Chinese Annals of Mathematics,Series B,2016,37(3):427-440.
4Cheng-xiu QIANG,Abdukadir OBUL.The Skew-commutator Relations and Grobner-Shirshov Bases of Quantum Group of Type c3[J].Acta Mathematicae Applicatae Sinica,2020,36(4):825-835.
5何钰星,阿布都卡的·吾甫.量子群Uq(D4)上不可约模的Grobner-Shirshov对[J].数学的实践与认识,2021,51(1):204-213.

1孔军士,阿布都卡的·吾甫.Z/3Z-量子群的Grbner-Shirshov基[J].中国科学：数学,2010,40(8):731-738.
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北京工业大学学报

2016年第4期

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量子群U_q(C_3)及其不可约模的Grbner-Shirshov基

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