Generalization of Yamagata's theorem on trivial extensions
type: Item
instance of: scholarly article
title: Generalization of Yamagata's theorem on trivial extensions
zbMATH Open document ID: 0634.16013
DOI: 10.1007/BF01196357
author: Andrzej Skowroński
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: Let A be a basic, connected finite dimensional algebra over an algebraically closed field K and let T(A) be the trivial extension of A by its minimal injective cogenerator Q. The author strengthens the result of \textit{K. Yamagata} [Lect. Notes Math. 903, 364-371 (1981; Zbl 0475.16016)] that T(A) is representation-infinite if the ordinary quiver of A contains an oriented cycle, by studying the zero-relations in this cycle and using the Galois covering \(\hat A\to T(A)\), where \(\hat A\) is the double infinite matrix algebra generated by A and Q in the sense of \textit{D. Hughes} and \textit{J. Waschbüsch} [Proc. Lond. Math. Soc., III. Ser. 46, 347-364 (1983; Zbl 0488.16021)].
Mathematics Subject Classification ID: 16Gxx
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 16S20
zbMATH DE Number: 4031898
zbMATH Keywords: connected finite dimensional algebra
zbMATH Keywords: trivial extension
zbMATH Keywords: minimal injective cogenerator
zbMATH Keywords: representation-infinite
zbMATH Keywords: quiver
zbMATH Keywords: Galois covering
zbMATH Keywords: double infinite matrix algebra
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01196357
OpenAlex ID: W1965295673
description: scientific article; zbMATH DE number 4031898