JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (10): 34-38.doi: 10.6040/j.issn.1671-9352.0.2021.697

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Linear independence of cluster monomials of cluster algebras of type G2 via categorification

GAO Xin-zhao, XIE Yun-li*   

  1. School of Mathematics, Southwest Jiaotong University, Chengdu 611756, Sichuan, China
  • Published:2022-10-06

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Abstract: Using the method of categorization, Fomin-Zelevinskys conjecture about the linear independence of cluster monomials in all cluster algebras holds for cluster algebras of type G2 is proved, by establishing the Caldero-Chapoton formula from the indecomposable rigid objects in the category of finitely generated modules of the cluster tilted algebra to the cluster variables of the corresponding cluster algebra.

Key words: cluster algebra, cluster monomial, cluster category, cluster tilted algebra, Caldero-Chapoton formula

CLC Number: 

  • O154.1
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