A geometric description of m-cluster categories
A geometric description of m-cluster categories
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DOI：
10.1090/s0002-9947-08-04441-3
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发表时间：
2006-07
影响因子：
1.3
通讯作者：
K. Baur;B. Marsh
中科院分区：
文献类型：
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作者：
K. Baur;B. Marsh
我们证明了An 1型的m-簇范畴等价于规则nm + 2-边形的对角线的几何定义范畴.这推广了Caldero，Chapoton和Schiffler f或m = 1的结果。该方法使用的理论，翻译颤动及其相应的网格类别。我们还介绍的概念的第m个权力的一个翻译，并显示它如何可以用来实现的m-集群类别的集群类别。
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 f or 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 can be used to realise the m-cluster category in terms of the cluster category.