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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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/997 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-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 |
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2025-12-02T15:29:03Z |
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2025-12-02T15:29:03Z |
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1850411922282774528 |