One class of representations over trivial extensions of iterated tilted algebras
type: Item
instance of: scholarly article
title: One class of representations over trivial extensions of iterated tilted algebras
zbMATH Open document ID: 0820.16012
author: Jie Xiao
author: Pu Zhang
published in: Tsukuba Journal of Mathematics
publication date: 1995-09-11T00:00:00Z
review text: The authors consider the following situation. Let \(k\) be an algebraically closed field and \(A\) be a finite dimensional iterated tilted algebra of type \(\vec{\Delta}\). Consider the trivial extension of \(A\), \(T(A) = A \bowtie D(A)\), where \(D\) denotes the usual duality \(\text{Hom}_ k(- ,k)\). The main results here concern \(T(A)\)-modules which belong to components of the Auslander-Reiten quiver of \(T(A)\) of the form \(\mathbb{Z} \vec{\Delta}\). Such modules are called modules on platform. They are not directing but enjoy very nice properties. To mention some of them: (i) the number of the modules on platform which have the same dimension vector is equal to or less than the number of simple \(A\)-modules; (ii) a module on platform is uniquely determined by its top and socle; (iii) a module on platform is uniquely determined by its Loewy factor and by its socle factor.
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 16D60
zbMATH DE Number: 515578
zbMATH Keywords: finite dimensional iterated tilted algebras
zbMATH Keywords: trivial extensions
zbMATH Keywords: duality
zbMATH Keywords: Auslander-Reiten quivers
zbMATH Keywords: modules on platform
zbMATH Keywords: simple \(A\)-modules
zbMATH Keywords: top
zbMATH Keywords: socle
zbMATH Keywords: Loewy factors
zbMATH Keywords: socle factors
reviewed by: Flávio U. Coelho
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162135
OpenAlex ID: W1942982193
DOI: 10.21099/TKBJM/1496162135
description: scientific article; zbMATH DE number 515578