Dimensions of finite type for representations of partially ordered sets

Dimensions of finite type for representations of partially ordered sets

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of finite type. We also characterize those dimensions of finite type...

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Date:2018
Main Authors: Drozd, Yuriy A., Kubichka, Eugene A.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
Representations of posets
finite type
indecomposable representations
16G20,16G60
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/997
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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-997
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-9972018-05-15T06:07:40Z Dimensions of finite type for representations of partially ordered sets Drozd, Yuriy A. Kubichka, Eugene A. Representations of posets, finite type, indecomposable representations 16G20,16G60 We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of finite type. We also characterize those dimensions of finite type, for which there is an indecomposable representation of this dimension, and show that there can be at most one indecomposable representation of any dimension of finite type. Moreover, if such a representation exists, it only has scalar endo-morphisms. These results (Theorem 1.6, page 25) generalize those of [5, 1, 9]. 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/997 Algebra and Discrete Mathematics; Vol 3, No 3 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/997/526 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 Representations of posets
finite type
indecomposable representations
16G20,16G60
spellingShingle Representations of posets
finite type
indecomposable representations
16G20,16G60
Drozd, Yuriy A.
Kubichka, Eugene A.
Dimensions of finite type for representations of partially ordered sets
topic_facet Representations of posets
finite type
indecomposable representations
16G20,16G60
format Article
author Drozd, Yuriy A.
Kubichka, Eugene A.
author_facet Drozd, Yuriy A.
Kubichka, Eugene A.
author_sort Drozd, Yuriy A.
title Dimensions of finite type for representations of partially ordered sets
title_short Dimensions of finite type for representations of partially ordered sets
title_full Dimensions of finite type for representations of partially ordered sets
title_fullStr Dimensions of finite type for representations of partially ordered sets
title_full_unstemmed Dimensions of finite type for representations of partially ordered sets
title_sort dimensions of finite type for representations of partially ordered sets
description We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of finite type. We also characterize those dimensions of finite type, for which there is an indecomposable representation of this dimension, and show that there can be at most one indecomposable representation of any dimension of finite type. Moreover, if such a representation exists, it only has scalar endo-morphisms. These results (Theorem 1.6, page 25) generalize those of [5, 1, 9].
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/997
work_keys_str_mv AT drozdyuriya dimensionsoffinitetypeforrepresentationsofpartiallyorderedsets
AT kubichkaeugenea dimensionsoffinitetypeforrepresentationsofpartiallyorderedsets
first_indexed 2025-07-17T10:30:47Z
last_indexed 2025-07-17T10:30:47Z
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