On the cluster category of a marked surface

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August undefined, 2024

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

Cluster algebras from surfaces

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 … 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 ... ipad change language back to english

Cotorsion pairs in the cluster category of a marked surface

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 … 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). 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 … ipad change weather location

The cluster category of a surface with punctures via group actions ...

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

Web1 de mar. de 2014 · We present examples of quasi-homomorphisms involving familiar cluster algebras, such as cluster structures on Grassmannians, and those associated … 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 ... ipad change default calendarWeb8 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 … ipad change keyboard type

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

On the cluster category of a marked surface

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

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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 … 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 … 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.

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

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 …

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] ipad change userWebThe 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) ... ipad change screen timeoutWebdecorated 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 … ipad change photo resolutionWeb6 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 … open lung approachWeb7 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 … openluchttheater thornWeb8 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. … open luggage lock combinationWebThis 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 open lung biopsy-recovery