REPETITIVE HIGHER CLUSTER CATEGORIES OF TYPE An

被引：2

作者：

Lamberti, Lisa ^{[1
]}

机构：

[1] ETHZ, Dept Math, CH-8092 Zurich, Switzerland

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2014年 / 13卷 / 02期

关键词：

Repetitive cluster categories; cluster categories; cluster combinatorics; triangulations of polygons; POLYGON DISSECTIONS; ALGEBRAS; COMPLEXES; QUIVERS;

D O I：

10.1142/S0219498813500916

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the repetitive higher cluster category of type A(n), defined as the orbit category D-b(mod kA(n))/(tau(-1)[m])(p), is equivalent to a category defined on a subset of diagonals in a regular polygon. This generalizes the construction of Caldero-Chapoton-Schiffler [Quivers with relations arising from clusters (A(n) case), Trans. Amer. Math. Soc. 358(3) (2006) 1347-1364], which we recover when p = m = 1, and the work of Baur-Marsh, [A geometric description of the m-cluster categories, Trans. Amer. Math. Soc. 360(11) (2008) 5789-5803], treating the case p = 1, m > 1. Our approach also leads to a geometric model of the bounded derived category in type A.

引用

页数：21

共 23 条

[1] ON THE STRUCTURE OF TRIANGULATED CATEGORIES WITH FINITELY MANY INDECOMPOSABLES [J].