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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.07323 |
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| _version_ | 1866918114714714112 |
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| author | Nkansah, David |
| author_facet | Nkansah, David |
| contents | We construct Nakayama functors on proper abelian subcategories of triangulated categories with a Serre functor using approximation theory. This, in turn, allows for the construction of Auslander-Reiten translates. As a result, we prove that suitable proper abelian subcategories are dualising $k$-varieties and have enough projectives if and only if they have enough injectives. As an application, we provide a new proof of the existence of Auslander-Reiten sequences in the category of finite dimensional modules over a finite dimensional algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07323 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nakayama functors on proper abelian subcategories Nkansah, David Representation Theory 18E10, 18G80 We construct Nakayama functors on proper abelian subcategories of triangulated categories with a Serre functor using approximation theory. This, in turn, allows for the construction of Auslander-Reiten translates. As a result, we prove that suitable proper abelian subcategories are dualising $k$-varieties and have enough projectives if and only if they have enough injectives. As an application, we provide a new proof of the existence of Auslander-Reiten sequences in the category of finite dimensional modules over a finite dimensional algebra. |
| title | Nakayama functors on proper abelian subcategories |
| topic | Representation Theory 18E10, 18G80 |
| url | https://arxiv.org/abs/2312.07323 |