English

An Infinitely Generated Upper Cluster Algebra

Representation Theory 2013-05-30 v1 Algebraic Geometry

Abstract

We show that upper cluster algebras need not be finitely generated, answering a question of Berenstein, Fomin and Zelevinsky. Our counter-example is a cluster algebra with B-matrix (033303330)\begin{pmatrix} 0 & 3 & -3 \\ -3 & 0 & 3 \\ 3 & -3 & 0 \end{pmatrix} and coefficients obeying a genericity condition.

Keywords

Cite

@article{arxiv.1305.6867,
  title  = {An Infinitely Generated Upper Cluster Algebra},
  author = {David E Speyer},
  journal= {arXiv preprint arXiv:1305.6867},
  year   = {2013}
}

Comments

3 pages

R2 v1 2026-06-22T00:24:41.167Z