THE CLUSTER CATEGORY OF A CANONICAL ALGEBRA

被引：36

作者：

Barot, M. ^{[1
]}

Kussin, D. ^{[2
]}

Lenzing, H. ^{[2
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

[2] Univ Gesamthsch Paderborn, Inst Math, D-33095 Paderborn, Germany

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 362卷 / 08期

关键词：

REPRESENTATIONS; EQUIVALENCES; CURVES;

D O I：

10.1090/S0002-9947-10-04998-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X. As an application we determine the automorphism group of the cluster category and show that the cluster-tilting objects form a cluster structure in the sense of Buan, Iyama, Reiten and Scott. The tilting graph of the sheaf category always coincides with the tilting or exchange graph of the cluster category. We show that this graph is connected if the Euler characteristic of X is non-negative, or equivalently, if A is of tame (domestic or tubular) representation type.

引用

页码：4313 / 4330

页数：18

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