Characteristic modules of quasi-hereditary algebras with three simples
type: Item
instance of: scholarly article
title: Characteristic modules of quasi-hereditary algebras with three simples
zbMATH Open document ID: 0887.16013
DOI: 10.1007/BF02882589
author: Pu Zhang
author: Yanan Lin
published in: Chinese Science Bulletin
publication date: 1998-03-15T00:00:00Z
review text: The main result of this note is the following: Let \(T\) be a generalized tilting module over a basic quasi-hereditary algebra \((A,\leq)\) with three simple modules and suppose that the indecomposable direct summands of \(T\) satisfy two conditions (to have unique `highest weight' and to be modules over certain quasi-hereditary quotient algebras of \(A\)) which are well-known to hold true for the characteristic tilting module of \(A\). Then \(T\) actually must be the characteristic tilting module of \((A,\leq)\). Reviewer's remark: The same result holds true without any assumption on the number of \(A\)-simples. This can be shown (by induction on the number of simples) using lemma 4 in the paper and the fact, that computing cohomology one may pass from \(A\) to a certain quasi-hereditary quotient algebra if the modules involved are defined over this quotient algebra.
Mathematics Subject Classification ID: 16G10
zbMATH DE Number: 1077938
zbMATH Keywords: generalized tilting modules
zbMATH Keywords: basic quasi-hereditary algebras
zbMATH Keywords: simple modules
zbMATH Keywords: indecomposable direct summands
zbMATH Keywords: quasi-hereditary quotient algebras
reviewed by: Steffen Koenig
MaRDI profile type: Publication
cites work: Q3804882
cites work: The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
cites work: Applications of contravariantly finite subcategories
cites work: Quasi-hereditary algebras and tilting modules
cites work: Q3934557
cites work: Cocovers and tilting modules
cites work: Almost Complete Tilting Modules
cites work: Complements to partial tilting modules
full work available at URL: https://doi.org/10.1007/bf02882589
OpenAlex ID: W2078177207
description: scientific article; zbMATH DE number 1077938