A construction of dual box
Let \({\mathtt R}\) be a quasi-hereditary algebra, \({\mathscr F} (\Delta)\) and \({\mathscr F}(\nabla)\) its categories of good and cogood modules correspondingly. In [6] these categories were characterized as the categories of representations of some boxes \({\mathscr A}={\mathscr A}_{\Delta}\)...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/890 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | Let \({\mathtt R}\) be a quasi-hereditary algebra, \({\mathscr F} (\Delta)\) and \({\mathscr F}(\nabla)\) its categories of good and cogood modules correspondingly. In [6] these categories were characterized as the categories of representations of some boxes \({\mathscr A}={\mathscr A}_{\Delta}\) and \({\mathscr A}_{\nabla}\). These last are the box theory counterparts of Ringel duality ([8]). We present an implicit construction of the box \({\mathscr B}\) such that \({\mathscr B}-{\mathrm{mo\,}}\) is equivalent to \({\mathscr F}(\nabla)\). |
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