The \(\Delta\)-filtered modules without self-extensions for the Auslander algebra of \(k[T]/\langle T^n\rangle\)
type: Item
instance of: scholarly article
title: The \(\Delta\)-filtered modules without self-extensions for the Auslander algebra of \(k[T]/\langle T^n\rangle\)
zbMATH Open document ID: 0971.16007
DOI: 10.1023/A:1009999006899
author: Thomas Brüstle
author: Lutz Hille
author: Claus Michael Ringel
author: Gerhard Röhrle
published in: Algebras and Representation Theory
publication date: 2001-06-12T00:00:00Z
review text: In an earlier paper [Transform. Groups 4, No. 1, 35-52 (1999; Zbl 0924.20035)], two of the present authors showed that the problem of describing conjugacy classes under the action of a parabolic subgroup of a general linear group acting on its unipotent radical, is equivalent to the problem of describing the \(\Delta\)-filtered modules over the Auslander algebra of \(k[T]/\langle T^n\rangle\) for some \(n\). The present paper studies these \(\Delta\)-filtered modules, in particular those without self-extensions which are classified in a purely combinatorial way. In fact, an indecomposable such module is determined by its \(\Delta\)-dimension vector.
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1385255
zbMATH Keywords: quasi-hereditary algebras
zbMATH Keywords: modules without self-extensions
zbMATH Keywords: filtered modules
zbMATH Keywords: indecomposable modules
reviewed by: Steffen Koenig
MaRDI profile type: Publication
full work available at URL: a:1009999006899
OpenAlex ID: W35249384
description: scientific article; zbMATH DE number 1385255