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Cluster algebras and triangulated orbifolds.

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.
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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/
Record Created:20 Jan 2016 14:35
Last Modified:26 Jul 2017 15:01

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