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.
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.
基金
supported by National Science Foundation of USA (Grant No. DMS1702115)
