Cluster algebras and triangulated orbifolds
Abstract
We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute growth rate of these cluster algebras, provide positivity of Laurent expansions of cluster variables, and prove sign-coherence of c-vectors.
Keywords
Cite
@article{arxiv.1111.3449,
title = {Cluster algebras and triangulated orbifolds},
author = {Anna Felikson and Michael Shapiro and Pavel Tumarkin},
journal= {arXiv preprint arXiv:1111.3449},
year = {2019}
}
Comments
58 pages, lots of figures; v4: the accepted version with further corrections (not included in the journal version): the definition of an arc on an orbifold is corrected (thanks to T. Nakanishi who has told us about the mistake), typos corrected, references to the paper of Fomin-Thurston updated (including the numbers of statements). arXiv admin note: text overlap with arXiv:1210.5569 by other authors