Upper cluster algebras and choice of ground ring

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（7）
• 页码范围: 1257-1266
• 页数: 10页
• 语种: 英文

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.