Stable equivalence of selfinjective algebras of tilted type
type: Item
instance of: scholarly article
title: Stable equivalence of selfinjective algebras of tilted type
zbMATH Open document ID: 0915.16005
published in: Archiv der Mathematik
publication date: 1999-07-05T00:00:00Z
review text: Let \(B\) be a tilted algebra not of Dynkin type and consider \(\widehat B\) its repetitive algebra. Denote by \(\nu_{\widehat B}\) the Nakayama automorphism of \(\widehat B\) and let \(\varphi\) be a positive automorphism of \(\widehat B\). Then the algebra given by the quotient \(\widehat B/(\varphi\nu_{\widehat B})\) is called a selfinjective algebra of tilted type. In the paper under review, the authors characterize these algebras. One of the results proven can be stated as follows: A selfinjective algebra \(A\) is stably equivalent to a selfinjective algebra \(\Lambda\) of tilted type if and only if \(A\) is socle equivalent to a selfinjective algebra \(\Lambda\) of tilted type. As a consequence they get the following corollary. Let \(A\) and \(\Lambda\) be two stably equivalent selfinjective algebras of tilted type. Then \(A\) and \(\Lambda\) have the same number of pairwise nonisomorphic simple modules.
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 16S70
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 1186711
zbMATH Keywords: tilted algebras
zbMATH Keywords: repetitive algebras
zbMATH Keywords: Nakayama automorphisms
zbMATH Keywords: stably equivalent selfinjective algebras of tilted type
zbMATH Keywords: simple modules
author: Andrzej Skowroński
author: Kunio Yamagata
reviewed by: Flávio U. Coelho
MaRDI profile type: Publication
full work available at URL: s000130050205
OpenAlex ID: W2008235702
DOI: 10.1007/S000130050205
description: scientific article; zbMATH DE number 1186711