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Chin. Phys. B, 2015, Vol. 24(1): 010201    DOI: 10.1088/1674-1056/24/1/010201
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Cluster algebra structure on the finite dimensional representations of affine quantum group Uq(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
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 Uq(Â3). As a conclusion, for every exchange relation of cluster algebra, there exists an exact sequence of the full subcategory corresponding to it.
Keywords:  affine quantum group      cluster algebra      monoidal categorification  
Received:  20 May 2014      Revised:  19 August 2014      Accepted manuscript online: 
PACS:  02.20.Uw (Quantum groups)  
  02.10.Hh (Rings and algebras)  
  03.65.Fd (Algebraic methods)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11475178).
Corresponding Authors:  Zheng Zhu-Jun     E-mail:  zhengzj@scut.edu.cn

Cite this article: 

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 Uq(Â3) 2015 Chin. Phys. B 24 010201

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