On the cluster category of a marked surface

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 … 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]

Cluster categories for marked surfaces: punctured case

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 … 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 … list t powershell https://group4materials.com

On the Cluster Category of a Marked Surface – arXiv Vanity

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). 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- 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. list travel agencies brooklyn

Cotorsion pairs in the cluster category of a marked surface

Category:Decorated marked surfaces (part B): topological realizations

Tags:On the cluster category of a marked surface

On the cluster category of a marked surface

Decorated marked surfaces (part B): topological realizations

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 … 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

Did you know?

WebarXiv:1311.0010v1 [math.RT] 31 Oct 2013 Clustercategoriesformarkedsurfaces:puncturedcase Yu Qiu and Yu Zhou Abstract We study the cluster categories arising from ... 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 ...

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) … 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 …

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 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 …

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, impact sustainability ltdWebtion 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 impact surgery drinkWeb1 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 … impact svbWeb1 de mar. de 2014 · We present examples of quasi-homomorphisms involving familiar cluster algebras, such as cluster structures on Grassmannians, and those associated … listtrac heartland mlsWeb15 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 … list tree bootstrapWeb(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). impact sweetenerWebCompositio Math.153 (2024) 1779{1819 doi:10.1112/S0010437X17007229 Cluster categories for marked surfaces: punctured case Yu Qiu and Yu Zhou Dedicated to … impact svg files