English

Positivity and tameness in rank 2 cluster algebras

Combinatorics 2019-11-01 v1

Abstract

We study the relationship between the positivity property in a rank 2 cluster algebra, and the property of such an algebra to be tame. More precisely, we show that a rank 2 cluster algebra has a basis of indecomposable positive elements if and only if it is of finite or affine type. This statement disagrees with a conjecture by Fock and Goncharov.

Keywords

Cite

@article{arxiv.1303.5806,
  title  = {Positivity and tameness in rank 2 cluster algebras},
  author = {Kyungyong Lee and Li Li and Andrei Zelevinsky},
  journal= {arXiv preprint arXiv:1303.5806},
  year   = {2019}
}