Auslander-Reiten translations in the monomorphism categories of exact categories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915633381244928 |
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| author | Luo, Xiu-Hua Zhu, Shijie |
| author_facet | Luo, Xiu-Hua Zhu, Shijie |
| contents | Let $Λ$ be a finite dimensional algebra. Let $\mathcal C$ be a functorially finite exact subcategory of $Λ$-mod with enough projective and injective objects and $\mathcal S (\mathcal C)$ be its monomorphism category. It turns out that the category $\mathcal S (\mathcal C)$ has almost split sequences. We show an explicit formula for the Auslander-Reiten translation in $\mathcal S (\mathcal C)$. Furthermore, if $\mathcal C$ is a stably $d$-Calabi-Yau Frobenius category, we calculate objects under powers of Auslander-Reiten translation in the triangulated category $\overline{\mathcal S(\mathcal C)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Auslander-Reiten translations in the monomorphism categories of exact categories Luo, Xiu-Hua Zhu, Shijie Representation Theory Category Theory 16G70, 18A20, 18A25, 16B50 Let $Λ$ be a finite dimensional algebra. Let $\mathcal C$ be a functorially finite exact subcategory of $Λ$-mod with enough projective and injective objects and $\mathcal S (\mathcal C)$ be its monomorphism category. It turns out that the category $\mathcal S (\mathcal C)$ has almost split sequences. We show an explicit formula for the Auslander-Reiten translation in $\mathcal S (\mathcal C)$. Furthermore, if $\mathcal C$ is a stably $d$-Calabi-Yau Frobenius category, we calculate objects under powers of Auslander-Reiten translation in the triangulated category $\overline{\mathcal S(\mathcal C)}$. |
| title | Auslander-Reiten translations in the monomorphism categories of exact categories |
| topic | Representation Theory Category Theory 16G70, 18A20, 18A25, 16B50 |
| url | https://arxiv.org/abs/2408.01359 |