| G2型丛代数中丛单项式线性无关性的范畴化证明 |
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| 引用本文： | 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. DOI: 10.6040/j.issn.1671-9352.0.2021.697 |
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| 作者姓名： | 高昕昭 谢云丽 |
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| 作者单位： | 西南交通大学数学学院, 四川 成都 611756 |
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| 基金项目： | 国家自然科学基金资助项目(12171397) |
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| 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。
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| 关 键 词： | 丛代数 丛单项式 丛范畴 丛倾斜代数 Caldero-Chapoton公式 |
Linear independence of cluster monomials of cluster algebras of type G2 via categorification |
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| GAO Xin-zhao,XIE Yun-li. Linear independence of cluster monomials of cluster algebras of type G2 via categorification[J]. Journal of Shandong University, 2022, 57(10): 34-38. DOI: 10.6040/j.issn.1671-9352.0.2021.697 |
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| Authors: | GAO Xin-zhao XIE Yun-li |
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| Affiliation: | School of Mathematics, Southwest Jiaotong University, Chengdu 611756, Sichuan, China |
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| Abstract: | Using the method of categorization, Fomin-Zelevinskys 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. |
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| Keywords: | cluster algebra cluster monomial cluster category cluster tilted algebra Caldero-Chapoton formula |
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