G2型丛代数中丛单项式线性无关性的范畴化证明

doi:10.6040/j.issn.1671-9352.0.2021.697

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 34-38.doi: 10.6040/j.issn.1671-9352.0.2021.697

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G2型丛代数中丛单项式线性无关性的范畴化证明

高昕昭,谢云丽^*

西南交通大学数学学院, 四川成都 611756

发布日期:2022-10-06
作者简介:高昕昭(1997— ),女,硕士研究生,研究方向为代数表示论. E-mail:xinzhao.gao1@gmail.com*通信作者简介:谢云丽(1979— ),女,博士,讲师,硕士生导师,研究方向为代数表示论. E-mail:xieyunli@swjtu.edu.cn
基金资助:
国家自然科学基金资助项目(12171397)

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

GAO Xin-zhao, XIE Yun-li^*

School of Mathematics, Southwest Jiaotong University, Chengdu 611756, Sichuan, China

Published:2022-10-06

摘要/Abstract

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G2型丛代数成立。

关键词: 丛代数, 丛单项式, 丛范畴, 丛倾斜代数, Caldero-Chapoton公式

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

中图分类号:

O154.1

高昕昭,谢云丽. G2型丛代数中丛单项式线性无关性的范畴化证明[J]. 《山东大学学报(理学版)》, 2022, 57(10): 34-38.

GAO Xin-zhao, XIE Yun-li. Linear independence of cluster monomials of cluster algebras of type G2 via categorification[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 34-38.

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G2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 G2 via categorification

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