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Cluster algebras and triangulated orbifolds (1111.3449v4)
Published 15 Nov 2011 in math.CO, math.GT, and math.RA
Abstract: 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.
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