Felikson, A. and Shapiro, M. and Tumarkin, P. (2012) 'Cluster algebras and triangulated orbifolds.', Advances in mathematics., 231 (5). pp. 2953-3002.
Abstract
We construct geometric realizations for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston [10] to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute the growth rate of these cluster algebras, provide the positivity of Laurent expansions of cluster variables, and prove the sign-coherence of View the MathML source-vectors.
| Item Type: | Article |
|---|---|
| Keywords: | Cluster algebra, Triangulated orbifold, Mutation, Unfolding. |
| Full text: | (AM) Accepted Manuscript Available under License - Creative Commons Attribution Non-commercial No Derivatives. Download PDF (820Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://doi.org/10.1016/j.aim.2012.07.032 |
| Publisher statement: | © 2012 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Date accepted: | 30 July 2012 |
| Date deposited: | 20 January 2016 |
| Date of first online publication: | December 2012 |
| Date first made open access: | No date available |
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