A Geometric Description of the m-cluster Categories of Type Dn
نویسندگان
چکیده
منابع مشابه
A Geometric Description of the m-cluster Categories of Type Dn
This category was introduced in [1] and has been studied by Assem, Brüstle, Schiffler and Todorov [2], the authors [3], Thomas [4], Wralsen [5] and Zhu [6]. In particular, Thomas and Zhu have shown that it gives rise to the combinatorics of the generalized cluster complexes of Fomin and Reading [7] (defined by Tzanaki [8] for types A and B). It is known that C∆ is triangulated [1], Krull-Schmid...
متن کاملA GEOMETRIC DESCRIPTION OF THE m - CLUSTER CATEGORIES OF TYPE
We show that the m-cluster category of type Dn is equivalent to a certain geometrically-defined category of arcs in a punctured regular nm − m + 1-gon. This generalises a result of Schiffler for m = 1. We use the notion of the mth power of a translation quiver to realise the m-cluster category in terms of the cluster category. Introduction Let k be a field and Q a quiver of Dynkin type ∆. Let D...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2010
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnm011