Cluster tilting for one-dimensional hypersurface singularities

被引：74

作者：

Burban, Igor ^{[2
]}

Iyama, Osamu ^{[1
]}

Keller, Bernhard ^{[3
]}

Reiten, Idun ^{[4
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[2] Johannes Gutenberg Univ Mainz, Fachbereich Phys Math & Informat, Inst Math, D-55099 Mainz, Germany

[3] Univ Paris 07, CNRS, UMR 7586, UFR Math, F-75251 Paris 05, France

[4] Norges Tekn Naturvitenskapelige Univ, Inst Matemat Fag, N-7491 Trondheim, Norway

来源：

ADVANCES IN MATHEMATICS | 2008年 / 217卷 / 06期

关键词：

cluster tilting; 2-Calabi-Yau categories;

D O I：

10.1016/j.aim.2007.10.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article We Study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for existence of cluster tilting objects and their complete description by homological methods, using higher almost split sequences and results from birational geometry. We obtain a large class of 2-CY tilted algebras which are finite-dimensional symmetric and satisfy tau(2) = id. In particular, we compute 2-CY tilted algebras for simple and minimally elliptic curve singularities. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：2443 / 2484

页数：42