Upper cluster algebras and choice of ground ring

作     者：Eric Bucher John Machacek Michael Shapiro 

作者机构：Department of Mathematics Xavier University Cincinnati OH 45207 USA Department of Mathematics and Statistics York University Toronto Ontario A13J 1P3 Canada Department of Mathematics Michigan State University East Lansing MI 48824 USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2019年第62卷第7期

页      面：1257-1266页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Science Foundation of USA (Grant No. DMS1702115) 

主　　题：cluster algebras upper cluster algebras locally acyclic cluster algebras 

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.