On the cluster category of a marked surface

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

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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 … 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). green dragon bishops frome

Cotorsion pairs in the cluster category of a marked surface

WebCompositio Math.153 (2024) 1779{1819 doi:10.1112/S0010437X17007229 Cluster categories for marked surfaces: punctured case Yu Qiu and Yu Zhou Dedicated to … 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 ... WebarXiv:1311.0010v1 [math.RT] 31 Oct 2013 Clustercategoriesformarkedsurfaces:puncturedcase Yu Qiu and Yu Zhou Abstract We study the cluster categories arising from ... green dragon bottomless brunch

[1005.2422] On the Cluster Category of a Marked Surface

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 Web1 de mar. de 2014 · We present examples of quasi-homomorphisms involving familiar cluster algebras, such as cluster structures on Grassmannians, and those associated … flt natures tableWeb7 de jan. de 2024 · To an unpunctured non-orientable marked surface, Dupont and Palesi introduced a commutative algebra analogous to the cluster algebras associated to orientable surfaces of Fomin-Shapiro-Thruston. The role of clusters in such an algebra is given by quasi-triangulations, that is, maximal collections of arcs and one-sided simple … fl to 44 cumberland island circle

"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) ... " - On the cluster category of a marked surface

On the cluster category of a marked surface

Extensions in Jacobian Algebras and Cluster Categories of Marked Surfaces

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 Web15 de jun. de 2024 · We study cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we …

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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 … Web7 de dez. de 2012 · We construct two bases for each cluster algebra coming from a triangulated surface without punctures. We work in the context of a coefficient system …

WebWe study in this paper the cluster category C (S, M) of a marked surface (S, M) without punctures. We explicitly describe the objects in C ( S , M ) as direct sums of homotopy … 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 …

Web30 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) … 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 …

Webnon 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).

Web13 de mai. de 2010 · We 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 … fl to 11221 john wycliffe wayWebdecorated 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 … green dragon breathing fireWebToday 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- fl to 530 north gulf rdWeb1 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 … green dragon buffet cheshireWebOn 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 ... green dragon brook new forestWeb7 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] fl to austin tx flightsWebtion 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 green dragon bungay facebook