Upper cluster algebras and choice of ground ring
Commutative Algebra
2019-10-04 v2
Abstract
We initiate a study of the dependence on the choice of ground ring on the question of 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.
Keywords
Cite
@article{arxiv.1802.04835,
title = {Upper cluster algebras and choice of ground ring},
author = {Eric Bucher and John Machacek and Michael Shapiro},
journal= {arXiv preprint arXiv:1802.04835},
year = {2019}
}
Comments
Accepted for publication in Special Topic on Cluster Algebras in Sci China Math