Cluster algebras and triangulated orbifolds

Details Cluster algebras and triangulated orbifolds Cluster algebras and triangulated orbifolds

2011-11-15

arxiv.org/abs/1111.3449v3

Mathematics

Combinatorics

54 pages, lots of figures; v3: a section about sign-coherence of c-vectors added, minor corrections

Scientific paper

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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