Cluster algebras and triangulated orbifolds

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

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.

Citation

Felikson, A., Shapiro, M., & Tumarkin, P. (2012). Cluster algebras and triangulated orbifolds. Advances in Mathematics, 231(5), 2953-3002. https://doi.org/10.1016/j.aim.2012.07.032

• 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
• DOI: https://doi.org/10.1016/j.aim.2012.07.032
• Keywords: Cluster algebra, Triangulated orbifold, Mutation, Unfolding.
• Public URL: https://durham-repository.worktribe.com/output/1478910