Cluster algebra structure on the finite dimensional representations of affine quantum group Uq(Â3)

doi:10.1088/1674-1056/24/1/010201

›› 2015, Vol. 24 ›› Issue (1): 10201-010201.doi: 10.1088/1674-1056/24/1/010201

• GENERAL • 下一篇

Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(Â₃)

杨彦敏, 马海涛, 林冰生, 郑驻军

Department of Mathematics, South China University of Technology, Guangzhou 510641, China

收稿日期:2014-05-20 修回日期:2014-08-19 出版日期:2015-01-05 发布日期:2015-01-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11475178).

Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(Â₃)

Yang Yan-Min (杨彦敏), Ma Hai-Tao (马海涛), Lin Bing-Sheng (林冰生), Zheng Zhu-Jun (郑驻军)

Department of Mathematics, South China University of Technology, Guangzhou 510641, China

Received:2014-05-20 Revised:2014-08-19 Online:2015-01-05 Published:2015-01-05
Contact: Zheng Zhu-Jun E-mail:zhengzj@scut.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11475178).

摘要/Abstract

摘要： In this paper, we prove one case of conjecture given by Hernandez and Leclerc. We give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group U_q(Â₃). As a conclusion, for every exchange relation of cluster algebra, there exists an exact sequence of the full subcategory corresponding to it.

关键词: affine quantum group, cluster algebra, monoidal categorification

Abstract: In this paper, we prove one case of conjecture given by Hernandez and Leclerc. We give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group U_q(Â₃). As a conclusion, for every exchange relation of cluster algebra, there exists an exact sequence of the full subcategory corresponding to it.

Key words: affine quantum group, cluster algebra, monoidal categorification

中图分类号: (Quantum groups)

02.20.Uw

02.10.Hh (Rings and algebras) 03.65.Fd (Algebraic methods)

杨彦敏, 马海涛, 林冰生, 郑驻军. Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(Â₃)[J]. , 2015, 24(1): 10201-010201.

Yang Yan-Min (杨彦敏), Ma Hai-Tao (马海涛), Lin Bing-Sheng (林冰生), Zheng Zhu-Jun (郑驻军). Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(Â₃)[J]. Chin. Phys. B, 2015, 24(1): 10201-010201.

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Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(Â₃)

Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(Â₃)

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