The Auslander-Reiten quiver of the category of m−periodic complexes

Chaio, Claudia; González Chaio, Alfredo; Pratti, Isabel; Souto Salorio, María José

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http://hdl.handle.net/2183/34511

The Auslander-Reiten quiver of the category of m−periodic complexes

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Souto_Salorio_MariaJose_2024_The_Auslander_Reiten_quiver_of_the_category_of_m_periodic_complexes.pdf (262.17 KB)

Identifiers

URI: http://hdl.handle.net/2183/34511

DOI: 10.1016/j.jpaa.2023.107569

Publication date

2024-05

Authors

Chaio, Claudia

González Chaio, Alfredo

Pratti, Isabel

Souto Salorio, María José

Bibliographic citation

Chaio, C., González Chaio, A., Pratti, I., & Souto Salorio, M. J. (2024). The Auslander-Reiten quiver of the category of m−periodic complexes. Journal of Pure and Applied Algebra, 228(5), 107569. doi:10.1016/j.jpaa.2023.107569

Abstract

[Abstract]: Let A be an additive k−category and C≡m(A) be the category of m−periodic complexes. For any integer m > 1, we study conditions under which the compression b functor Fm : C (A) → C≡m(A) preserves or reflects irreducible morphisms. Moreover, we find sufficient conditions for the functor Fm to be a Galois G-covering in the sense of [3]. If in addition A is a dualizing category then C≡m(A) has almost split sequences. In particular, for a finite dimensional algebra A with finite strong global dimension we determine how to build the Auslander-Reiten quiver of the category C≡m(proj A). Furthermore, we study the behavior of sectional paths in C≡m(proj A), when A is a finite dimensional algebra over a field k.

Description

©2024. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/. This version of the article: Chaio, C., González Chaio, A., Pratti, I., & Souto Salorio, M. J. (2024). “The Auslander-Reiten quiver of the category of m−periodic complexes.” has been accepted for publication in Journal of Pure and Applied Algebra, 228(5), 107569. The Version of Record is available online at https://doi.org/10.1016/j.jpaa.2023.107569.