A geometric description of $m$-cluster categories
نویسندگان
چکیده
منابع مشابه
A 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 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 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 کاملCLUSTER ALGEBRAS AND CLUSTER CATEGORIES
These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...
متن کاملCLUSTER CATEGORIES, m-CLUSTER CATEGORIES AND DIAGONALS IN POLYGONS
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.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-08-04441-3