Cluster algebras and triangulated orbifolds

Anna Felikson, Michael Shapiro, Pavel Tumarkin
2012 Advances in Mathematics  
2012) 'Cluster algebras and triangulated orbifolds.', Advances in mathematics., 231 (5). pp. 2953-3002. Further information on publisher's website: http://dx.Additional information: Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the
more » ... etadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full DRO policy for further details. Abstract. We construct geometric realizations for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston [FT] 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 c-vectors.
doi:10.1016/j.aim.2012.07.032 fatcat:cpidconavfbxvaco4boctv3x7u