On the cluster category of a marked surface
WebOn the cluster category of a marked surface without punctures Thomas Brüstle and Jie Zhang: Vol. 5 (2011), No. 4, 529–566 DOI: 10.2140/ant.2011.5.529. Abstract: We study the cluster category C (S, M) of a marked surface (S, M) without punctures. We explicitly describe the objects ...
On the cluster category of a marked surface
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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 … Web7 de mai. de 2012 · By using this result, we prove that there are no non-trivial $t-$structures in the cluster categories when the surface is connected. Based on this result, we give …
WebThis paper is the last in a series on decorated marked surfaces ([Q2, Q3, QZ1, BQZ, QZ2]). We construct a moduli space of framed quadratic differentials for a decorated marked surface, that is isomorphic to the space of stability conditions on the 3-Calabi-Yau (3-CY) category associated to the surface. We introduce the cluster exchange WebOn the cluster category of a marked surface without punctures, Algebra Number Theory 5 (2011), no. 4, 529-566, DOI 10.2140/ant.2011.5.529, zbl 1250.16013, MR2870100, arxiv 1005.2422. [BuDr]. I. Burban and Y. Drozd. On the derived categories of gentle and skew-gentle algebras: Homological algebra and matrix problems.
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- Web29 de jan. de 2024 · In this paper we construct a geometric model for the bounded derived category of a gentle algebra. The construction is based on the ribbon graph associated to a gentle algebra by the third author. This ribbon graph gives rise to an oriented surface with boundary and marked points in the boundary. We show that the homotopy classes of …
Web13 de mai. de 2010 · We study extension spaces, cotorsion pairs and their mutations in the cluster category of a marked surface without punctures.
Web20 de jun. de 2024 · In this section let C (S, M) be the cluster category of a marked surface (S, M) where all marked points lie in the boundary of S and each boundary … greek hello translationWeb1 de mar. de 2014 · We present examples of quasi-homomorphisms involving familiar cluster algebras, such as cluster structures on Grassmannians, and those associated … flow diagram of a websiteWebCluster Categories from Surfaces We consider in this talk the cluster category of a marked surface, explicitly describing the objects and the Auslander-Reiten structure in geometric terms. We further show that the objects without self-extensions correspond to curves without self-intersections. greek helmet feather clipartWeb(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). greek hedonist philosopherWeb15 de out. de 2024 · There exists a class of cluster algebras associated to oriented bordered surfaces with marked points. In [4], the authors describe the process by which … flow diagram of javaWeb1 de jan. de 2011 · As a first step towards finding an additive categorification of Dupont and Palesi's quasi-cluster algebras associated marked non-orientable surfaces, we study a … greek hellenic museum chicagoWebAcknowledgements First and foremost, I am very grateful for my advisor Gregg Musiker, without whom this thesis would not have been possible. He introduced me to cluster algebras a flow diagram of hvac system