Two-step tilting for standardly stratified algebras

Two-step tilting for standardly stratified algebras

We study the class of standardly stratified algebras introduced by Cline, Parshall and Scott, and its subclass of the so-called weakly properly stratified algebras, which generalizes the class of properly stratified algebras introduced by Dlab. We char-acterize when the Ringel dual of a standardly s...

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Bibliographic Details
Date:2018
Main Author: Frisk, Anders
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
stratified algebra
two-step tilting
finitistic dimension
16E10
16G10
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/998
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-998
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-9982018-05-15T06:07:40Z Two-step tilting for standardly stratified algebras Frisk, Anders stratified algebra, two-step tilting, finitistic dimension 16E10, 16G10 We study the class of standardly stratified algebras introduced by Cline, Parshall and Scott, and its subclass of the so-called weakly properly stratified algebras, which generalizes the class of properly stratified algebras introduced by Dlab. We char-acterize when the Ringel dual of a standardly stratified algebra is weakly properly stratified and show the existence of a two-step tilting module. This allows us to calculate the finitistic dimension of such algebras. Finally, we also give a construction showing that each finite partially pre-ordered set gives rise to a weakly properly stratified algebras with a simple preserving duality. Lugansk National Taras Shevchenko University 2018-05-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/998 Algebra and Discrete Mathematics; Vol 3, No 3 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/998/527 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-05-15T06:07:40Z
collection OJS
language English
topic stratified algebra
two-step tilting
finitistic dimension
16E10
16G10
spellingShingle stratified algebra
two-step tilting
finitistic dimension
16E10
16G10
Frisk, Anders
Two-step tilting for standardly stratified algebras
topic_facet stratified algebra
two-step tilting
finitistic dimension
16E10
16G10
format Article
author Frisk, Anders
author_facet Frisk, Anders
author_sort Frisk, Anders
title Two-step tilting for standardly stratified algebras
title_short Two-step tilting for standardly stratified algebras
title_full Two-step tilting for standardly stratified algebras
title_fullStr Two-step tilting for standardly stratified algebras
title_full_unstemmed Two-step tilting for standardly stratified algebras
title_sort two-step tilting for standardly stratified algebras
description We study the class of standardly stratified algebras introduced by Cline, Parshall and Scott, and its subclass of the so-called weakly properly stratified algebras, which generalizes the class of properly stratified algebras introduced by Dlab. We char-acterize when the Ringel dual of a standardly stratified algebra is weakly properly stratified and show the existence of a two-step tilting module. This allows us to calculate the finitistic dimension of such algebras. Finally, we also give a construction showing that each finite partially pre-ordered set gives rise to a weakly properly stratified algebras with a simple preserving duality.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/998
work_keys_str_mv AT friskanders twosteptiltingforstandardlystratifiedalgebras
first_indexed 2025-07-17T10:34:55Z
last_indexed 2025-07-17T10:34:55Z
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