G_(2)型丛代数中丛单项式线性无关性的范畴化证明  

Linear independence of cluster monomials of cluster algebras of type G_(2) via categorification

作　　者：高昕昭 谢云丽[1] GAO Xin-zhao;XIE Yun-li(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,Sichuan,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《山东大学学报（理学版）》2022年第10期34-38,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12171397)。

摘　　要：利用范畴化的方法,通过建立从丛倾斜代数的有限生成模范畴中不可分解的刚性对象,到对应的丛代数中丛变量的Caldero-Chapoton公式,证明Fomin-Zelevinsky关于丛代数中丛单项式的线性无关猜想对G型丛代数成立。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 Gis 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.

关 键 词：丛代数 丛单项式 丛范畴 丛倾斜代数 Caldero-Chapoton公式 

分 类 号：O154.1[理学—数学]