n-representation-finite algebras and twisted fractionally Calabi-Yau algebras

被引：46

作者：

Herschend, Martin ^{[1
]}

Iyama, Osamu ^{[1
]}

机构：

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

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2011年 / 43卷

关键词：

MODULES; CATEGORIES; QUIVERS;

D O I：

10.1112/blms/bdq101

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study n-representation-finite algebras from the viewpoint of the fractionally Calabi-Yau property. We shall show that all n-representation-finite algebras are twisted fractionally Calabi-Yau. We also show that for any l > 0, twisted (n(l-1)/l)-Calabi-Yau algebras of global dimension at most n are n-representation-finite. As an application, we give a construction of n-representation-finite algebras using the tensor product.

引用

页码：449 / 466

页数：18

共 42 条

[1] CLUSTER CATEGORIES FOR ALGEBRAS OF GLOBAL DIMENSION 2 AND QUIVERS WITH POTENTIAL [J].

Amiot, Claire .

ANNALES DE L INSTITUT FOURIER, 2009, 59 (06) :2525-2590

[2]

[Anonymous], 1988, Triangulated Categories in the Representation Theory of Finite-Dimensional Algebras. London Mathematical Society Lecture Notes Series

[3]

Auslander M, 1971, Queen Mary College Mathematics Notes

[4]

BONDAL AI, 1989, MATH USSR IZV+, V53, P519

[5] Cluster structures for 2-Calabi-Yau categories and unipotent groups [J].

Buan, A. B. ;

Iyama, O. ;

Reiten, I. ;

Scott, J. .

COMPOSITIO MATHEMATICA, 2009, 145 (04) :1035-1079

[6] 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

[7]

DELAPENA JA, 2009, LECT C SPECTR METH R

[8] Maximal n-orthogonal modules for selfinjective algebras [J].

Erdmann, Karin ;

Holm, Thorsten .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (09) :3069-3078

[9]

Gabriel P., 1980, Lect. Notes Math., V831, P1

[10]

Gei C., 2007, ARXIVMATH0703039 ARXIVMATH0703039

← 1 2 3 4 5 →