Classification of the Auslander-Reiten quivers of local Gorenstein orders and a characterization of the simple curve singularities
type: Item
instance of: scholarly article
title: Classification of the Auslander-Reiten quivers of local Gorenstein orders and a characterization of the simple curve singularities
zbMATH Open document ID: 0597.16009
DOI: 10.1016/0022-4049(86)90115-5
author: Alfred Wiedemann
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: This paper contains a complete list of all finite Auslander-Reiten quivers of local Gorenstein orders over a complete Dedekind domain of finite lattice type. For each translation quiver \(\Gamma\) in this list, a Gorenstein order \(\Lambda\) is explicitly indicated, with \(\Gamma\) as its Auslander-Reiten quiver. In each case, indecomposable \(\Lambda\)-lattices are described.
reviewed by: Constantin Năstăsescu
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16Gxx
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 3961871
zbMATH Keywords: finite Auslander-Reiten quivers
zbMATH Keywords: local Gorenstein orders
zbMATH Keywords: finite lattice type
zbMATH Keywords: indecomposable \(\Lambda \) -lattices
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90115-5
OpenAlex ID: W2057563953
cites work: REMARKS ON THE STATIONARY PHASE METHOD AND COXETER NUMBERS
cites work: Q3941572
cites work: Replication Numbers for Non-Dynkin Sectional Subgraphs in Finite Auslander-Reiten Quivers and Some Properties of Weyl Roots
cites work: Critical simply connected algebras
cites work: Covering spaces in representation-theory
cites work: Die Auflösung der rationalen Singularitäten holomorpher Abbildungen
cites work: Q3922829
cites work: Construction of Auslander-Reiten quivers for a class of group rings
cites work: The Auslander-Reiten Quiver of a Simple Curve Singularity
cites work: Q5551539
cites work: Q3889229
cites work: Group representations without groups
cites work: Integral representations and diagrams
cites work: Einfache Kurvensingularitäten und torsionsfreie Moduln
cites work: Q3890860
cites work: Algebren, Darstellungsköcher, Überlagerungen und zurück
cites work: Q3903139
cites work: Diagrammatic methods in the representation theory of orders
cites work: The structure over \(\mathbb{Z}[q,q^{-1}]\) of Hecke orders of dihedral groups
cites work: Auslander-Reiten species of Bäckström orders
cites work: Simple singularities and simple algebraic groups
cites work: Q5587150
cites work: Orders with loops in their auslander-reiten graph
cites work: The Auslander-Reiten graph of integral blocks with cyclic defect two and their integral representations
cites work: The existence of covering functors for orders and consequences for stable components with oriented cycles
cites work: An Integral Version of the Igusa-Todorov Algorithm
description: scientific article; zbMATH DE number 3961871