CLUSTER CATEGORIES, m-CLUSTER CATEGORIES AND DIAGONALS IN POLYGONS
نویسنده
چکیده
The goals of this expository article are on one hand to describe how to construct (m-) cluster categories from triangulations (resp. from m+2angulations) of polygons. On the other hand, we explain how to use translation quivers and their powers to obtain the m-cluster categories directly from the diagonals of a polygon.
منابع مشابه
Geometric Construction of Cluster Algebras and Cluster Categories
In this note we explain how to obtain cluster algebras from triangulations of (punctured) discs following the approach of [FST06]. Furthermore, we give a description of m-cluster categories via diagonals (arcs) in (punctured) polygons and of m-cluster categories via powers of translation quivers as given in joint work with R. Marsh ([BM08a], [BM07]).
متن کاملGeometric Methods in Representation Theory Fock Space Representations Fock Space Representations of U Q ( Sl N )
Articles-Karin BAUR: Cluster categories, m-cluster categories and diagonals in polygons-Ada BORALEVI: On simplicity and stability of tangent bundles of rational homogeneous varieties-Laurent EVAIN: Intersection theory on punctual Hilbert schemes-Daniel JUTEAU, Carl MAUTNER and Geordie WILLIAMSON: Perverse sheaves and modular representation theory-Manfred LEHN and Christoph SORGER: A symplectic ...
متن کاملA GEOMETRIC DESCRIPTION OF m-CLUSTER CATEGORIES
We show that the m-cluster category of type An−1 is equivalent to a certain geometrically-defined category of diagonals of a regular nm+ 2-gon. This generalises a result of Caldero, Chapoton and Schiffler for m = 1. The approach uses the theory of translation quivers and their corresponding mesh categories. We also introduce the notion of the mth power of a translation quiver and show how it ca...
متن کاملA geometric model for cluster categories of type Dn
We give a geometric realization of cluster categories of type Dn using a polygon with n vertices and one puncture is its center as a model. In this realization, the indecomposable objects of the cluster category correspond to certain homotopy classes of paths between two vertices. 0 Introduction Cluster categories were introduced in [BMRRT] and, independently, in [CCS1] for type An, as a means ...
متن کاملChu connections and back diagonals between $\mathcal{Q}$-distributors
Chu connections and back diagonals are introduced as morphisms for distributors between categories enriched in a small quantaloid Q. These constructions, meaningful for closed bicategories, are dual to that of arrow categories and the Freyd completion of categories. It is shown that, for a small quantaloid Q, the category of complete Q-categories and left adjoints is a retract of the dual of th...
متن کامل