Auslander-Reiten translations in the monomorphism categories of exact categories
Abstract
Let $\Lambda$ be a finite dimensional algebra. Let $\mathcal C$ be a functorially finite exact subcategory of $\Lambda$-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 $\overline{\mathcal S(\mathcal C)}$.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.01359
- arXiv:
- arXiv:2408.01359
- Bibcode:
- 2024arXiv240801359L
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Category Theory;
- 16G70;
- 18A20;
- 18A25;
- 16B50
- E-Print:
- 26 pages