A geometric model for cluster categories of type D n
نویسندگان
چکیده
منابع مشابه
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A 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 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...
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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 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...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2007
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-007-0071-6