WebToday cluster algebras are connected to various elds of mathematics, in-cluding Combinatorics (polyhedra, frieze patterns, green sequences, snake graphs, T-paths, dimer models, triangulations of surfaces) Representation theory of nite dimensional algebras (cluster categories, cluster-tilted algebras, preprojective algebras, tilting theory, 2-Calbi- WebThe Cluster Category of a Marked Surface II Ryan Kinser (University of Connecticut) 2/2/11. Cluster Algebras Seminar Quivers with potentials 0 (Canceled due to snow) ...
Cluster categories for marked surfaces: punctured case
Web(2024) Decorated Marked Surfaces III: The Derived Category of a Decorated Marked Surface. International mathematics research notices. volum 2024 (17). ... (2011) AN INTRODUCTION TO HIGHER CLUSTER CATEGORIES. Bulletin of the Iranian Mathematical Society (BIMS). volum 37 (2). Web31 de out. de 2013 · We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we … how do you pronounce ushuaia argentina
On the cluster category of a marked surface without punctures
Web8 de fev. de 2024 · 1 Introduction. Cluster algebras were introduced by Fomin and Zelevinsky [Reference Fomin and Zelevinsky FZ02] as a class of commutative algebras equipped with a combinatorial structure relating different subsets of the algebra called clusters.Since then, there has been a great interest in cluster algebras and their … WebCluster algebras were introduced by Fomin and Zelevinsky in 2002 in [FZ1] in order to give an algebraic framework for the study of the (dual) canonical bases in Lie theory. This work was further developed in [BFZ, FZ2, FZ4].Cluster algebras are commutative algebras given by generators, the cluster variables, and relations.The construction of the generators is … Webon the marked surface correspond to the cluster variables of this cluster algebra, and that mutations correspond to flips of arcs. In [2] it is shown for unpunctured surfaces that the Jacobian algebra of the associated quiver with potential is gentle. D. Labardini generalizes in [44] the definition of a potential to punctured surfaces, how do you pronounce van alstyne