Cluster algebras and triangulated orbifolds [article]

Anna Felikson, Michael Shapiro, Pavel Tumarkin
2014 arXiv   pre-print
We construct geometric realization 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 growth rate of these cluster algebras, provide positivity of Laurent expansions of cluster variables, and prove sign-coherence of c-vectors.
arXiv:1111.3449v4 fatcat:oczjlhj2zzfe5ekzqgjfaolwmi