A geometric description of m-cluster categories

被引：49

作者：

Baur, Karin ^{[1
]}

Marsh, Robert J. ^{[2
]}

机构：

[1] Univ Leicester, Dept Math, Leicester LE1 7RH, Leics, England

[2] Univ Leeds, Dept Pure Math, Leeds LS2 9JT, W Yorkshire, England

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 360卷 / 11期

基金：

英国工程与自然科学研究理事会;

关键词：

cluster category; m-cluster category; polygon dissection; m-divisible; cluster algebra; simplicial complex; mesh category; diagonal; Auslander-Reiten quiver; derived category; triangulated category;

D O I：

10.1090/S0002-9947-08-04441-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the m-cluster category of type A(n-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 m-th power of a translation quiver and show how it can be used to realise the m-cluster category in terms of the cluster category.

引用

页码：5789 / 5803

页数：15

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