On fully wild categories of representations of posets
Assume that \(I\) is a finite partially ordered set and \(k\) is a field. We prove that if the category \(\mbox{ prin}(kI)\) of prinjective modules over the incidence \(k\)-algebra \(kI\) of \(I\) is fully \(k\)-wild then the category \({\bf fpr}(I,k)\) of finite dimensional \(k\)-representations of...
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| Date: | 2018 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/899 |
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-8992018-03-21T07:07:28Z On fully wild categories of representations of posets Kasjan, Stanislaw representations of posets, wild, fully wild representation type, endofunctors of wild module category 16G60, 16G30, 03C60 Assume that \(I\) is a finite partially ordered set and \(k\) is a field. We prove that if the category \(\mbox{ prin}(kI)\) of prinjective modules over the incidence \(k\)-algebra \(kI\) of \(I\) is fully \(k\)-wild then the category \({\bf fpr}(I,k)\) of finite dimensional \(k\)-representations of \(I\) is also fully \(k\)-wild. A key argument is a construction of fully faithful exact endofunctors of the category of finite dimensional \(k\langle x,y\rangle\)-modules, with the image contained in certain subcategories. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/899 Algebra and Discrete Mathematics; Vol 5, No 3 (2006) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/899/428 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-03-21T07:07:28Z |
| collection |
OJS |
| language |
English |
| topic |
representations of posets wild fully wild representation type endofunctors of wild module category 16G60 16G30 03C60 |
| spellingShingle |
representations of posets wild fully wild representation type endofunctors of wild module category 16G60 16G30 03C60 Kasjan, Stanislaw On fully wild categories of representations of posets |
| topic_facet |
representations of posets wild fully wild representation type endofunctors of wild module category 16G60 16G30 03C60 |
| format |
Article |
| author |
Kasjan, Stanislaw |
| author_facet |
Kasjan, Stanislaw |
| author_sort |
Kasjan, Stanislaw |
| title |
On fully wild categories of representations of posets |
| title_short |
On fully wild categories of representations of posets |
| title_full |
On fully wild categories of representations of posets |
| title_fullStr |
On fully wild categories of representations of posets |
| title_full_unstemmed |
On fully wild categories of representations of posets |
| title_sort |
on fully wild categories of representations of posets |
| description |
Assume that \(I\) is a finite partially ordered set and \(k\) is a field. We prove that if the category \(\mbox{ prin}(kI)\) of prinjective modules over the incidence \(k\)-algebra \(kI\) of \(I\) is fully \(k\)-wild then the category \({\bf fpr}(I,k)\) of finite dimensional \(k\)-representations of \(I\) is also fully \(k\)-wild. A key argument is a construction of fully faithful exact endofunctors of the category of finite dimensional \(k\langle x,y\rangle\)-modules, with the image contained in certain subcategories. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/899 |
| work_keys_str_mv |
AT kasjanstanislaw onfullywildcategoriesofrepresentationsofposets |
| first_indexed |
2025-07-17T10:31:44Z |
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2025-07-17T10:31:44Z |
| _version_ |
1837890141337681920 |