A geometric model for cluster categories of type Dn

被引：59

作者：

Schiffler, Ralf ^{[1
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2008年 / 27卷 / 01期

关键词：

cluster category; triangulated surface; punctured polygon; elementary move;

D O I：

10.1007/s10801-007-0071-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a geometric realization of cluster categories of type D-n using a polygon with n vertices and one puncture in 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.

引用

页码：1 / 21

页数：21

共 25 条

[1] Cluster categories and duplicated algebras [J].

Assem, I. ;

Brustle, T. ;

Schiffler, R. ;

Todorov, G. .

JOURNAL OF ALGEBRA, 2006, 305 (01) :548-561

[2]

Assem I., 2006, ELEMENTS REPRESENTAT

[3]

ASSEM I, 2006, M CLUSTER CATEGORIES

[4]

Auslander M., 1995, CAMBRIDGE STUDIES AD, V36

[5]

BAUR K, 2006, IN PRESS T AM MATH S

[6]

BUAN A, IN PRESS P AM MATH S

[7]

Buan AB, 2007, T AM MATH SOC, V359, P323

[8] Tilting theory and cluster combinatorics [J].

Buan, Aslak Bakke ;

Marsh, Bethany Rose ;

Reineke, Markus ;

Reiten, Idun ;

Todorov, Gordana .

ADVANCES IN MATHEMATICS, 2006, 204 (02) :572-618

[9] Quivers with relations arising from clusters (An case) [J].

Caldero, P ;

Chapoton, F ;

Schiffler, R .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (03) :1347-1364

[10]

CALDERO P, IN PRESS ANN SCI ECO

← 1 2 3 →