Gr&#246;bner-Shirshov Basis of Quantum Group <italic>U<sub>q</sub></italic>(<italic>C</italic><sub>3</sub>) and Its Irreducible Modules

GAO Zhenzhen; YANG Shilin; WUFU Abudoukade

doi:10.11936/bjutxb2015060053

Journal of Beijing University of Technology > 2016 > 42(4): 632-636. > DOI: 10.11936/bjutxb2015060053

GAO Zhenzhen, YANG Shilin, WUFU Abudoukade. Gröbner-Shirshov Basis of Quantum Group U_q(C₃) and Its Irreducible Modules[J]. Journal of Beijing University of Technology, 2016, 42(4): 632-636. DOI: 10.11936/bjutxb2015060053

Citation:

PDF (834 KB)

Gröbner-Shirshov Basis of Quantum Group U_q(C₃) and Its Irreducible Modules

1. College of Applied Sciences,Beijing University of Technology, Beijing 100124, China;
2. College of Mathematics and System Sciences,Xinjiang University, Urumqi 830046, China

More Information

Received Date: June 17, 2015
Available Online: January 10, 2023

Graphical Abstract

Abstract

Abstract

Based on Auslander-Reiten theory of valued graph C₃ and Gröbner-Shirshov bases for representation theory,First by using the Ringel-Hall algebra approach,a Gröbner-Shirshov basis of quantum group U_q(C₃) was constructed. Then, a Gröbner-Shirshov basis of finite dimensional irreducible modules of U_q(C₃) was given by using double free module and composition lemma.
- quantum group,
- Grö,
- bner-Shirshov basis,
- double free modules

FullText(HTML)

References (15)

References

[1]	BUCHBERGER B.An algorithm for finding a basis for the residue class ring of a zero-dimensional ideal[D].Innsbruck:University of Innsbruck,1965.
[2]	BERGMAN G M.The diamond lemma for ring theory[J].Advances in Mathematics,1978,29(2):178-218.
[3]	SHIRSHOV A I.Some algorithmic problems for Lie algebras[J].Siberian Math J,1962,3:292-296.
[4]	BOKUT L A,MALCOLMSON P.Gröbner-Shirshov bases for quantum enveloping algebras[J].Israel Journal of Mathematics,1996,96(1):97-113.
[5]	YUNUS G,OBUL A.Gröbner-Shirshov basis of quantum group of type D₄[J].Chin Ann Math:B,2011,32(4):581-592.
[6]	KONG J S,OBUL A.Gröbner-Shirshov basis of quantum group of type B₂[J].Southeast Asian Bulletin of Mathematics,2010,34:693-704.
[7]	KANG S J,LEE K H.Gröbner-Shirshov basis for representation theory[J].J Korean Math Soc,2000,37(1):55-72.
[8]	KANG S J,LEE K H.Gröbner-Shirshov bases for irreducible SL_n+1 modules[J].Journal of Algebra,2000,232(1):1-20.
[9]	CHIBRIKOV E S.On free Lie conformal algebras[J].Journal of Novosibirsk State University,2004,4(1):65-83.
[10]	CHEN Y Q,CHEN Y S,ZHONG C Y.Compositiondiomond lemma for modules[J].Czechoslovak Math,2010,60(135):59-76.
[11]	DRINFEL'D V G.Hopf algebras and the quantum YangBaxter equation[J].Doklady Akademii Nauk SSSR,1985,283(5):1060-1064.
[12]	DEND B M,DU J,PARSHAL B,et al.Finite dimensional algebra and quantum groups[M].Mathematical Surveys and Monographs:Volume 150.Providence:Amer Math Soc,2008:157-175..
[13]	RINGEL C M.PBW-bases of quantum groups[J].J Reine Angew Math,1996,470:51-88.
[14]	JANTZEN J C.Lectures on Quantum groups[M].Graduate Studies in Mathematics:Volume 6.Providence:Amer Math Soc,1996:31-87.
[15]	RINGEL C M.Hall algebras and quantum groups[J].Invent Math,1990,101:583-592.

Cited By

Cited by

Periodical cited type(8)

1.	梁旭华，刘杨，李雨润. 大型十字交叉地铁车站结构地震响应分析. 粉煤灰综合利用. 2024(03): 106-112 .
2.	马晓明，苗晗，蒋录珍，安军海. 竖向地震动对地铁车站共构结构体系地震响应的影响研究. 城市轨道交通研究. 2024(09): 139-146+153 .
3.	盛杰. 不同地震类型作用下多跨地铁车站结构的地震响应. 黑龙江科技大学学报. 2022(04): 474-480 .
4.	潘婷婷，胡雪平，任天翔，徐博. 纵横波时差耦合作用下地铁车站地震响应分析. 地质力学学报. 2022(04): 596-604 .
5.	黎思成，李原，靳金平，陶连金，丁鹏. 大型地下管沟复杂节点结构地震响应规律. 地下空间与工程学报. 2022(S2): 926-933 .
6.	伍国韬，赵洪波，刘元珍，王凯. 平行地铁车站结构的地震响应特性. 黑龙江科技大学学报. 2021(01): 122-128 .
7.	韩学川，陶连金，安韶，张宇，史明. 邻近地面建筑一体化地铁车站结构地震响应分析. 北京工业大学学报. 2021(04): 338-345 . 本站查看
8.	于仲洋，张鸿儒，邱滟佳，李昊. 无缝换乘地铁车站的地震响应特性研究. 湖南大学学报(自然科学版). 2021(11): 166-176 .

Other cited types(8)

Get Citation

PDF

XML

Article views (19) PDF downloads (6) Cited by(16)

Turn off MathJax

Article Contents

Abstract

References

Gröbner-Shirshov Basis of Quantum Group Uq(C3) and Its Irreducible Modules

Abstract

References

Cited by

Periodical cited type(8)

Other cited types(8)

Catalog

Export File

Citation

Format

Content

Gröbner-Shirshov Basis of Quantum Group U_q(C₃) and Its Irreducible Modules