On the cluster category of a marked surface

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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 … 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 without punctures

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 Web1 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 … fire extinguisher service melbourne

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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- Web7 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 … etched rtic tumbler

$S arXiv:1212.0007v3 [math.RT] 5 Nov 2014$

On a category of cluster algebras - ScienceDirect

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 … Webon the generalized cluster category associated to a surface Swith marked points and non-empty boundary, which generalizes Bru¨stle-Zhang’s result for the puncture free case. As an application, we show that the intersection of the shifts in the 3-Calabi-Yau derived category D(ΓS) associated tothe surface and the corresponding Seidel-Thomas fire extinguisher service miles city mtWebarXiv:1311.0010v1 [math.RT] 31 Oct 2013 Clustercategoriesformarkedsurfaces:puncturedcase Yu Qiu and Yu Zhou Abstract We study the cluster categories arising from ... fire extinguisher service montgomery alabama

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

On the cluster category of a marked surface

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 · 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 …

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Web1 de out. de 2013 · The cluster category of a marked surface. Let (S, M) be a marked surface without punctures, i.e. S is a compact oriented Riemann surface with ∂ S ≠ ∅ and … 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 …

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] 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 …

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 … 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 …

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 …

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) … etched saw bladeWeb20 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 … etched rose bud vaseWebnon 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). fire extinguisher service near katy txWeb1 Introduction. Cluster algebras and quiver mutation were introduced by Fomin and Zelevinsky [8], and (additive) categorification of such structures, often in terms of … fire extinguisher service near 77586WebCluster 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. fire extinguisher service near rockville mdWebCompositio Math.153 (2024) 1779{1819 doi:10.1112/S0010437X17007229 Cluster categories for marked surfaces: punctured case Yu Qiu and Yu Zhou Dedicated to … fire extinguisher service near springboro ohWeb15 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 … etched rock address