Auslander-Reiten translations in the monomorphism categories of exact categories
Xiu-Hua Luo, Shijie Zhu

TL;DR
This paper investigates the structure of monomorphism categories derived from exact categories over finite dimensional algebras, providing explicit formulas for Auslander-Reiten translations and exploring their behavior in Calabi-Yau contexts.
Contribution
It offers an explicit formula for Auslander-Reiten translation in monomorphism categories of exact categories and analyzes their properties in Calabi-Yau Frobenius categories.
Findings
Existence of almost split sequences in monomorphism categories.
Explicit formula for Auslander-Reiten translation in these categories.
Calculation of objects under powers of translation in Calabi-Yau settings.
Abstract
Let be a finite dimensional algebra. Let be a functorially finite exact subcategory of -mod with enough projective and injective objects and be its monomorphism category. It turns out that the category has almost split sequences. We show an explicit formula for the Auslander-Reiten translation in . Furthermore, if is a stably -Calabi-Yau Frobenius category, we calculate objects under powers of Auslander-Reiten translation in the triangulated category .
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry
