Outputs (27)

Skew-symmetric cluster algebras of finite mutation type (2012)
Journal Article
Felikson, A., Shapiro, M., & Tumarkin, P. (2012). Skew-symmetric cluster algebras of finite mutation type. Journal of the European Mathematical Society, 14(4), 1135-1180. https://doi.org/10.4171/jems/329

In the famous paper [FZ2] Fomin and Zelevinsky obtained Cartan-Killing type classification of all cluster algebras of finite type, i.e. cluster algebras having only finitely many distinct cluster variables. A wider class of cluster algebras is formed... Read More about Skew-symmetric cluster algebras of finite mutation type.

Cluster algebras of finite mutation type via unfoldings (2012)
Journal Article
Felikson, A., Shapiro, M., & Tumarkin, P. (2012). Cluster algebras of finite mutation type via unfoldings. International Mathematics Research Notices, 2012(8), 1768-1804. https://doi.org/10.1093/imrn/rnr072

We complete the classification of mutation-finite cluster algebras by extending the technique derived by Fomin, Shapiro, and Thurston to skew-symmetrizable case. We show that for every mutation-finite skew-symmetrizable matrix a diagram characterizin... Read More about Cluster algebras of finite mutation type via unfoldings.

Automorphism groups of root systems matroids (2011)
Journal Article
Dutour Sikirić, M., Felikson, A., & Tumarkin, P. (2011). Automorphism groups of root systems matroids. European Journal of Combinatorics, 32(3), 383-389. https://doi.org/10.1016/j.ejc.2010.11.003

Given a root system View the MathML source, the vector system View the MathML source is obtained by taking a representative v in each antipodal pair {v,−v}. The matroid View the MathML source is formed by all independent subsets of View the MathML so... Read More about Automorphism groups of root systems matroids.

Reflection subgroups of Coxeter groups (2010)
Journal Article
Felikson, A., & Tumarkin, P. (2010). Reflection subgroups of Coxeter groups. Transactions of the American Mathematical Society, 362(2), 847-858. https://doi.org/10.1090/s0002-9947-09-04859-4

Coxeter polytopes with a unique pair of non-intersecting facets (2009)
Journal Article
Felikson, A., & Tumarkin, P. (2009). Coxeter polytopes with a unique pair of non-intersecting facets. Journal of Combinatorial Theory, Series A, 116(4), 875-902. https://doi.org/10.1016/j.jcta.2008.10.008

Regular subalgebras of affine Kac–Moody algebras (2008)
Journal Article
Felikson, A., Retakh, A., & Tumarkin, P. (2008). Regular subalgebras of affine Kac–Moody algebras. Journal of Physics A: Mathematical and Theoretical, 41(36), Article 365204. https://doi.org/10.1088/1751-8113/41/36/365204

On hyperbolic Coxeter polytopes with mutually intersecting facets. (2008)
Journal Article
Felikson, A., & Tumarkin, P. (2008). On hyperbolic Coxeter polytopes with mutually intersecting facets. Journal of Combinatorial Theory, Series A, 115(1), 121-146. https://doi.org/10.1016/j.jcta.2007.04.006