The Nakayama automorphism of a self-injective preprojective algebra

被引：3

作者：

Grant, Joseph ^{[1
]}

机构：

[1] Univ East Anglia, Sch Math, Norwich Res Pk, Norwich NR4 7TJ, Norfolk, England

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2020年 / 52卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

16D50; 16E60 (primary); 16G10; 16G70 (secondary); REPRESENTATION-FINITE ALGEBRAS;

D O I：

10.1112/blms.12313

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a simple proof, using Auslander-Reiten theory, that the preprojective algebra of a basic hereditary algebra of finite representation type is Frobenius. We then describe its Nakayama automorphism, which is induced by the Nakayama functor on the module category of our hereditary algebra.

引用

页码：137 / 152

页数：16

共 24 条

[1]

[Anonymous], LECT NOTES PURE APPL

[2]

AUSLANDER M, 1997, CAMBRIDGE STUDIES AD, V36

[3]

AUSLANDER M., 1996, REPRESENTATION THEOR, V18, P39

[4] THE PREPROJECTIVE ALGEBRA OF A TAME HEREDITARY ARTIN ALGEBRA [J].

BAER, D ;

GEIGLE, W ;

LENZING, H .

COMMUNICATIONS IN ALGEBRA, 1987, 15 (1-2) :425-457

[5] Periodic algebras which are almost Koszul [J].

Brenner, S ;

Butler, MCR ;

King, AD .

ALGEBRAS AND REPRESENTATION THEORY, 2002, 5 (04) :331-367

[6]

BUChwEITz R.-O., 1998, Contemp. Math., V229, P81

[7] Preprojective algebras, differential operators and a Conze embedding for deformations of Kleinian singularities [J].

Crawley-Boevey, W .

COMMENTARII MATHEMATICI HELVETICI, 1999, 74 (04) :548-574

[8] The Nakayama Automorphism of the Almost Calabi-Yau Algebras Associated to SU(3) Modular Invariants [J].

Evans, David E. ;

Pugh, Mathew .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2012, 312 (01) :179-222

[9] CORRECTION [J].

GABRIEL, P .

MANUSCRIPTA MATHEMATICA, 1972, 6 (03) :309-&

[10]

Gabriel P., 1980, LECT NOTES MATH, P1

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