On the cluster category of a marked surface

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August undefined, 2024

WebAcknowledgements 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 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 ...

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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] 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. … citizenship 2008 civics test

On the Cluster Category of a Marked Surface Request PDF

Web1 Introduction. Cluster algebras and quiver mutation were introduced by Fomin and Zelevinsky [8], and (additive) categorification of such structures, often in terms of … Web15 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 … 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 … citizenship 2008 test

The self-folded triangle and the corresponding tagged version

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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 … WebCompositio Math.153 (2024) 1779{1819 doi:10.1112/S0010437X17007229 Cluster categories for marked surfaces: punctured case Yu Qiu and Yu Zhou Dedicated to … citizenship 2018 paper 2Web30 de nov. de 2024 · This is a survey on the project `Decorated Marked Surfaces', where we introduce the decoration on a marked surfaces , to study Calabi-Yau-2 (cluster) … dickey\u0027s tree service delaware

"Web13 de mai. de 2010 · We study extension spaces, cotorsion pairs and their mutations in the cluster category of a marked surface without punctures. " - On the cluster category of a marked surface

On the cluster category of a marked surface

Ginzburg algebras of triangulated surfaces and perverse schobers

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 … 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).

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WebCluster 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. 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

WebGinzburg algebras associated to triangulated surfaces provide a means to categorify the cluster algebras of these surfaces. As shown by Ivan Smith, the ﬁnite derived category of such a Ginzburg algebra can be embedded into the Fukaya category of the total space of a Lefschetz ﬁbration over the surface. Inspired by this perspective, we Webtion of a marked surface. On the other hand, the categoriﬁcation of cluster algebras leads to cluster categories of acyclic quivers due to Buan, Marsh, Reineke, Reiten and Todorov [12] and later to generalized cluster categories of quivers with potential due to Amiot [2], where mutations of cluster tilting objects model mutations of clusters. In

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- Web31 de out. de 2013 · Download PDF Abstract: We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed …

Webdecorated 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 … citizenship 2018 paper 1Web15 de jun. de 2024 · We study cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we … citizenship 2020 practice testWebon 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, citizenship 2019 paper 1 edexcelWebOn 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. dickey\\u0027s turkeyWeb1 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 … citizenship 2020 youtubeWebnon empty boundary, and Mbe a nite set of points (called marked points) on the boundary of such that there is at least one marked point on each boundary component of . We assume moreover that ( ;M) is not a disc with 1 or 2 marked points. The aim of this section is to give the de nition of the cluster algebra associated to the marked surface ( ;M). citizenship 2019 paper 1Web8 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 … citizenship 2020