Upper cluster algebras and choice of ground ring

被引：5
|
作者：
Bucher, Eric [1 ]
Machacek, John [2 ]
Shapiro, Michael [3 ]
机构：
[1] Xavier Univ, Dept Math, Cincinnati, OH 45207 USA
[2] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada
[3] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA
来源：
SCIENCE CHINA-MATHEMATICS | 2019年 / 62卷 / 07期
基金：
美国国家科学基金会;
关键词：
cluster algebras; upper cluster algebras; locally acyclic cluster algebras; BELAVIN-DRINFELD DATA; MINIMAL SIZE; SLN;
D O I：
10.1007/s11425-018-9486-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We initiate a study of the dependence of the choice of ground ring on the problem on whether a cluster algebra is equal to its upper cluster algebra. A condition for when there is equality of the cluster algebra and upper cluster algebra is given by using a variation of Muller's theory of cluster localization. An explicit example exhibiting dependence on the ground ring is provided. We also present a maximal green sequence for this example.
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页码：1257 / 1266
页数：10
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