On the cluster category of a marked surface

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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 … 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

On a category of cluster algebras - ScienceDirect

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 … 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- can i connect bluetooth to this device

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

On the cluster category of a marked surface without punctures

Cotorsion pairs in the cluster category of a marked surface

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. … 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 … fit plus familyWeb(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). fit plus offingen

"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 " - On the cluster category of a marked surface

On the cluster category of a marked surface

Cotorsion pairs in the cluster category of a marked surface

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

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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 … 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 …

Web1 de mai. de 2024 · On the cluster category of a marked surface without punctures. Article. Jan 2011; Thomas Brüstle; Jie Zhang; We study the cluster category C-(S,C-M) of a marked surface (S, M) without punctures. 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.

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 ... 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

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 …

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, can i connect ezonics usb camera to androidWebThe 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) ... can i connect extender to routerWebWe study the cluster category C (S,M) C ( S, M) of a marked surface (S,M) ( S, M) without punctures. We explicitly describe the objects in C (S,M) C ( S, M) as direct sums of … fit plus facebookWebGinzburg 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 can i connect fitbit to echelon bikeWeb30 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) … can i connect cpu to tvWebWe 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 … can i connect directly to modemWeb7 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] fitplus health club gachibowli