Properly stratified endomorphism algebras.
type: Item
instance of: scholarly article
title: Properly stratified endomorphism algebras.
zbMATH Open document ID: 1070.16015
author: Xueqing Chen
author: Vlastimil Dlab
published in: Journal of Algebra
publication date: 2005-04-07T00:00:00Z
review text: The authors prove the following statement: Theorem. Let \(R\) be a commutative, local, self-injective algebra over an algebraically closed field. Let \({\mathcal X}=\{X(1)=R,X(2),\dots,X(n)\}\) be a sequence of local-colocal \(R\)-modules reflecting inclusions of the corresponding local ideals \(\underline X(i)\) of \(R\) (i.e. \(\underline X(i)\subset\underline X(j)\) implies \(j\leq i\)). Let \(X=\bigoplus_{i=1}^nX(i)\) and \(A=\text{End}_R(X)\). Then the algebra \(A\) is properly stratified with respect to the natural order on \(\{1,\dots,n\}\) if and only if: (1) \(\underline X(i)\cap\underline X(j)\) is generated by suitable \(\underline X(t)\) for all \(i,j\); and (2) \(\underline X(j)\cap(\sum_{t=j+1}^n\underline X(t))=\sum_{t=j+1}^n(\underline X(j)\cap\underline X(t))\) for all \(j\).
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 2153353
zbMATH Keywords: properly stratified algebras
zbMATH Keywords: endomorphism algebras
zbMATH Keywords: quasi-hereditary algebras
zbMATH Keywords: standard modules
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.09.002
OpenAlex ID: W1985716702
Wikidata QID: Q105656645
cites work: Q3842816
cites work: Stratifying endomorphism algebras
cites work: Q4338466
cites work: Properly stratified algebras
cites work: Quasi-Hereditary Endomorphism Algebras
cites work: Categories of induced modules and standardly stratified algebras
cites work: Perverse Sheaves and ℂ ∗ -Actions
cites work: On a theorem of V. Dlab
cites work: Kategorie O , Perverse Garben Und Moduln Uber Den Koinvariantez Zur Weylgruppe
DOI: 10.1016/J.JALGEBRA.2004.09.002
description: scientific article; zbMATH DE number 2153353