Cluster algebras and triangulated orbifolds

By Anna Felikson, Michael Shapiro, Pavel Tumarkin. 2011

74 citations recorded by the source corpus.

Abstract We construct geometric realizations for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston [10] 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dee7e7119ec5ad526300a198d6834cb4252a1a05

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Ilke Çanakçi
2. Ralf Schiffler
3. Kyungyong Lee
4. Gregg Musiker
5. I. Reiten
6. Ben Davison
7. B. Keller
8. Osamu Iyama

In Geometry and Topology

1. Ilke Çanakçi
2. Ralf Schiffler
3. Kyungyong Lee
4. Gregg Musiker
5. I. Reiten
6. Ben Davison
7. B. Keller
8. Osamu Iyama

In Statistical and Nonlinear Physics

1. Ilke Çanakçi
2. Ralf Schiffler
3. Kyungyong Lee
4. Ben Davison
5. Dylan Rupel
6. Max Glick

Citations in the corpus

• Positivity for cluster algebras (2013, background): “The construction and the proof of the positivity conjecture have been generalized to non skew-symmetric cluster algebras from orbifolds in [10].”
• Snake graph calculus and cluster algebras from surfaces II: self-crossing snake graphs (2014, background): “For generalizations to the skew-symmetrizable case see [7,8].”