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- 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 …
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 … 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 … small heart pendant
Bases for cluster algebras from surfaces Compositio Mathematica ...
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 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 … 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). small heart picture frame