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}
}