On class groups of upper cluster algebras

被引：0
|
作者：
Pompili, Mara [1 ]
机构：
[1] Karl Franzens Univ Graz, Dept Math & Sci Comp, NAWI Graz, Heinrichstr 36, A-8010 Graz, Austria
来源：
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2025年
基金：
奥地利科学基金会;
关键词：
Cluster algebras; upper cluster algebras; factorization theory; class groups;
D O I：
10.4153/S0008414X25000033
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We compute the class groups of full rank upper cluster algebras in terms of the exchange polynomials. This characterizes the UFDs among these algebras. Our results simultaneously generalize theorems of Garcia Elsener, Lampe, and Smertnig from 2019 and of Cao, Keller, and Qin from 2023. Furthermore, we show that every (upper) cluster algebra is a finite factorization domain.
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页数：21
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