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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.


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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Publisher statement:© 2012 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
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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