On the cluster category of a marked surface

Author: cxwn

August undefined, 2024

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. 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 …

arXiv:2004.11136v3 [math.RT] 28 Dec 2024

Web13 de mai. de 2010 · We study extension spaces, cotorsion pairs and their mutations in the cluster category of a marked surface without punctures. 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 … chili\u0027s san angelo texas

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 … 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 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 chili\u0027s salad nutrition facts

On a category of cluster algebras - ScienceDirect

Cluster exchange groupoids and framed quadratic differentials

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 … 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 … chili\\u0027s scheduleWebOn 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 ... grace burkhart obituary

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

On the cluster category of a marked surface

Geometric and homological methods in representation theory

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, 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.

Did you know?

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 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 …

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) ... 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 …

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. … 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 …

Web6 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 …

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 grace burke oak ridge national lab chili\u0027s salisbury mdWeb1 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 … chili\u0027s salem new hampshireWeb31 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 … grace burke ornlWebon 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, chili\u0027s searcy arWebCompositio Math.153 (2024) 1779{1819 doi:10.1112/S0010437X17007229 Cluster categories for marked surfaces: punctured case Yu Qiu and Yu Zhou Dedicated to … chili\u0027s salt lake city utWeb8 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 … chili\u0027s salisbury md menu