English

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