On the cluster category of a marked surface
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. 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 …
On the cluster category of a marked surface
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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 … 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 ...
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 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 …
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 … 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 …
Web1 de mar. de 2014 · We present examples of quasi-homomorphisms involving familiar cluster algebras, such as cluster structures on Grassmannians, and those associated …
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 … churches ankeny iowaWebon 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, devansh bavishichurches angleseyWebToday 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- churches anglicanWeb31 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 … devansh birth certificateWebWe 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 … churches angola inWeb6 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 … devansh bhatt