On 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 … 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 …

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Web1 de mar. de 2014 · We present examples of quasi-homomorphisms involving familiar cluster algebras, such as cluster structures on Grassmannians, and those associated … 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 … how many bison are in north dakota https://serranosespecial.com

Bases for cluster algebras from surfaces Compositio …

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 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 ... 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 how many bison on catalina island

CLUSTER ALGEBRAS, REPRESENTATION THEORY, AND

Category:[1812.00008] Decorated Marked Surfaces: Calabi-Yau categories …

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On the cluster category of a marked surface

On the Cluster Category of a Marked Surface - NASA/ADS

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 … 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 …

On the cluster category of a marked surface

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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) … 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 …

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

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 … 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 …

WebWe 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 …

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 ... how many bison are on catalina islandWeb1 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 … high potassium foods patient educationWebThis 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 how many bit computer am i runningWebarXiv:1311.0010v1 [math.RT] 31 Oct 2013 Clustercategoriesformarkedsurfaces:puncturedcase Yu Qiu and Yu Zhou Abstract We study the cluster categories arising from ... high potassium foods national kidneyWebnon 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). how many bit in 1 kbWeb13 de mai. de 2010 · We study extension spaces, cotorsion pairs and their mutations in the cluster category of a marked surface without punctures. how many bison in yellowstone parkWebon 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, how many bit addresses are there in ipv4