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On the cluster category of a marked surface

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 https://mdbrich.com

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

[1005.2422] On the Cluster Category of a Marked Surface

Category:Extensions in Jacobian algebras and cluster categories of marked …

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On the cluster category of a marked surface

On the cluster category of a marked surface without punctures

WebWe study in this paper the cluster category C(S,M) of a marked surface (S,M). We explicitly describe the objects in C(S,M) as direct sums of homotopy classes of curves in (S,M) and one-parameter families related to closed curves in (S,M). Moreover, we describe the Auslander-Reiten structure of the category C(S,M) in geometric terms and show that … WebWe give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface $\mathbf{S}$ with marked points and non-empty boundary ...

On the cluster category of a marked surface

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Web1 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 … Web7 de dez. de 2012 · Bases for cluster algebras from surfaces - Volume 149 Issue 2. Skip to main content Accessibility help ... On the cluster category of a marked surface, Algebra Number Theory, to appear, arXiv:1005.2422.Google Scholar [BMRRT06]

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 … 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 …

Web1 de mar. de 2014 · We present examples of quasi-homomorphisms involving familiar cluster algebras, such as cluster structures on Grassmannians, and those associated … 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 ...

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

Web8 de out. de 2024 · Abstract. Given a certain triangulation of a punctured surface with boundary, we construct a new triangulated surface without punctures which covers it. … how do you pronounce urogynecologyWeb15 de jun. de 2024 · We study cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we … phone number for direct express debit cardWeb6 de jul. de 2024 · On the cluster category of a marked surface without punctures. T. Brustle, Jie Zhang. Mathematics. 2011. We study in this paper the cluster category C … phone number for direct lineWeb7 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 … how do you pronounce valencia in spanishWeb1 de mar. de 2014 · We study rooted cluster algebras and rooted cluster morphisms which were introduced in [1] recently and cluster structures in 2-Calabi–Yau triangulated categories. An example of rooted cluster morphism which is not ideal is given, this clarifying a doubt in [1].We introduce the notion of freezing of a seed and show that an … how do you pronounce utz potato chipsWebAcknowledgements 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 how do you pronounce vercruysseWebdecorated marked surface to the original marked surface; 4 the shift functor for the silting sets in the perfect category as the universal rotation in the marked mappingclass groupof decoratedmarked surface, whichgeneralizes the result in … how do you pronounce venetia