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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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/899 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
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