Invariance of selfinjective algebras of quasitilted type under stable equivalences.
type: Item
instance of: scholarly article
title: Invariance of selfinjective algebras of quasitilted type under stable equivalences.
zbMATH Open document ID: 1100.16011
published in: Manuscripta Mathematica
publication date: 2006-03-21T00:00:00Z
review text: This paper provides the final step in proving that the class of self-injective algebras of quasi-tilted type is closed under stable or derived equivalences. By a major result of \textit{D. Happel} [Invent. Math. 144, No. 2, 381-398 (2001; Zbl 1015.18006)], quasi-tilted algebras are either of tilted type or of canonical type. Passing to their repetitive algebras and then taking quotients modulo admissible automorphisms, one obtains the self-injective algebras of quasi-tilted type, which again are either of tilted or of canonical type. \textit{A. Skowroński} and \textit{K. Yamagata} have already shown [in Proc. Am. Math. Soc. 132, No. 3, 659-667 (2004; Zbl 1065.16016) and in Algebr. Represent. Theory 9, No. 1, 33-45 (2006; Zbl 1119.16010)] the stable and derived invariance of self-injective algebras of tilted type. The paper under review settles the remaining case of canonical type, by a detailed analysis of the representation theory of these algebras.
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16G70
zbMATH DE Number: 5014050
zbMATH Keywords: self-injective algebras
zbMATH Keywords: stable equivalences
zbMATH Keywords: derived equivalences
zbMATH Keywords: quasi-tilted algebras
author: Otto Kerner
author: Andrzej Skowroński
author: Kunio Yamagata
reviewed by: Steffen Koenig
MaRDI profile type: Publication
full work available at URL: s00229-005-0623-9
OpenAlex ID: W2091286412
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Invariance of selfinjective algebras of quasitilted type under stable equivalences. (DOI)
DOI: 10.1007/S00229-005-0623-9