Outputs (27)

Exhange graphs for mutation-finite non-integer quivers (2023)
Journal Article
Felikson, A., & Lampe, P. (2023). Exhange graphs for mutation-finite non-integer quivers. Journal of Geometry and Physics, 188, Article 104811. https://doi.org/10.1016/j.geomphys.2023.104811

Skew-symmetric non-integer matrices with real entries can be viewed as quivers with noninteger arrow weights. Such quivers can be mutated following the usual rules of quiver mutation. Felikson and Tumarkin show that mutation-finite non-integer quiver... Read More about Exhange graphs for mutation-finite non-integer quivers.

Cluster algebras of finite mutation type with coefficients (2023)
Journal Article
Felikson, A., & Tumarkin, P. (in press). Cluster algebras of finite mutation type with coefficients. Journal of combinatorial algebra,

We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type. This completes the classification of all mutation-finite cluster algebras started in [FeSTu1].

Mutation-finite quivers with real weights (2023)
Journal Article
Felikson, A., & Tumarkin, P. (2023). Mutation-finite quivers with real weights. Forum of Mathematics, Sigma, 11, Article e9. https://doi.org/10.1017/fms.2023.8

We classify all mutation-finite quivers with real weights. We show that every finite mutation class not originating from an integer skew-symmetrisable matrix has a geometric realisation by reflections. We also explore the structure of acyclic represe... Read More about Mutation-finite quivers with real weights.

Friezes for a pair of pants (2022)
Journal Article
Canakci, I., Garcia Elsener, A., Felikson, A., & Tumarkin, P. (2022). Friezes for a pair of pants. Séminaire lotharingien de combinatoire, 86B, Article 32

Frieze patterns are numerical arrangements that satisfy a local arithmetic rule. These arrangements are actively studied in connection to the theory of cluster algebras. In the setting of cluster algebras, the notion of a frieze pattern can be genera... Read More about Friezes for a pair of pants.

Cluster algebras from surfaces and extended affine Weyl groups (2021)
Journal Article
Felikson, A., Lawson, J., Shapiro, M., & Tumarkin, P. (2021). Cluster algebras from surfaces and extended affine Weyl groups. Transformation Groups, 26(2), 501-535. https://doi.org/10.1007/s00031-021-09647-y

We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space V , and with every triangul... Read More about Cluster algebras from surfaces and extended affine Weyl groups.

Infinite rank surface cluster algebras (2019)
Journal Article
Canakci, I., & Felikson, A. (2019). Infinite rank surface cluster algebras. Advances in Mathematics, 352, 862-942. https://doi.org/10.1016/j.aim.2019.06.008

We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite mutation... Read More about Infinite rank surface cluster algebras.

Geometry of mutation classes of rank 3 quivers (2019)
Journal Article
Felikson, A., & Tumarkin, P. (2019). Geometry of mutation classes of rank 3 quivers. Arnold Mathematical Journal, 5(1), 37-55. https://doi.org/10.1007/s40598-019-00101-2

We present a geometric realization for all mutation classes of quivers of rank 3 with real weights. This realization is via linear reflection groups for acyclic mutation classes and via groups generated by π-rotations for the cyclic ones. The geometr... Read More about Geometry of mutation classes of rank 3 quivers.

Acyclic cluster algebras, reflection groups, and curves on a punctured disc (2018)
Journal Article
Felikson, A., & Tumarkin, P. (2018). Acyclic cluster algebras, reflection groups, and curves on a punctured disc. Advances in Mathematics, 340, 855-882. https://doi.org/10.1016/j.aim.2018.10.020

We establish a bijective correspondence between certain non-self-intersecting curves in an n-punctured disc and positive c-vectors of acyclic cluster algebras whose quivers have multiple arrows between every pair of vertices. As a corollary, we obtai... Read More about Acyclic cluster algebras, reflection groups, and curves on a punctured disc.

Bases for cluster algebras from orbifolds (2017)
Journal Article
Felikson, A., & Tumarkin, P. (2017). Bases for cluster algebras from orbifolds. Advances in Mathematics, 318, 191-232. https://doi.org/10.1016/j.aim.2017.07.025

We generalize the construction of the bracelet and bangle bases defined in [36] and the band basis defined in [43] to cluster algebras arising from orbifolds. We prove that the bracelet bases are positive, and the bracelet basis for the affine cluste... Read More about Bases for cluster algebras from orbifolds.

Double Pants Decompositions Revisited (2017)
Journal Article
Felikson, A., & Natanzon, S. (2017). Double Pants Decompositions Revisited. Moscow mathematical journal, 17(1), 51-58

Double pants decompositions were introduced by the authors in 2011, together with a flip-twist groupoid acting on these decompositions. It was shown that flip-twist groupoid acts transitively on a certain topological class of the decompositions, howe... Read More about Double Pants Decompositions Revisited.