Publication details for Pavel TumarkinFelikson, A., Shapiro, M. & Tumarkin, P. (2012). Cluster algebras and triangulated orbifolds. Advances in Mathematics 231(5): 2953-3002.
- Publication type: Journal Article
- ISSN/ISBN: 0001-8708, 1090-2082
- DOI: 10.1016/j.aim.2012.07.032
- Keywords: Cluster algebra, Triangulated orbifold, Mutation, Unfolding.
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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.