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  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.
|Keywords:||Cluster algebra, Triangulated orbifold, Mutation, Unfolding.|
|Full text:||(AM) Accepted Manuscript|
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|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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