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Cluster algebras and triangulated orbifolds

Felikson, A.; Shapiro, M.; Tumarkin, P.

Cluster algebras and triangulated orbifolds Thumbnail


M. Shapiro


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.


Felikson, A., Shapiro, M., & Tumarkin, P. (2012). Cluster algebras and triangulated orbifolds. Advances in Mathematics, 231(5), 2953-3002.

Journal Article Type Article
Acceptance Date Jul 30, 2012
Publication Date Dec 1, 2012
Deposit Date Mar 19, 2012
Publicly Available Date Jan 20, 2016
Journal Advances in Mathematics
Print ISSN 0001-8708
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 231
Issue 5
Pages 2953-3002
Keywords Cluster algebra, Triangulated orbifold, Mutation, Unfolding.


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