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

2023/04/10 by Chaio, Claudia, Chaio, Alfredo González, Pratti, Isabel +1
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2304.04844

Abstract

Let A be an additive k-category and C_{≡ m}(A) be the category of m-periodic objects. For any integer m>1, we study conditions under which the compression functor \mathcal F_m :C^b(A) → C_{≡ m}(A) preserves or reflects irreducible morphisms. Moreover, we find sufficient conditions for the functor \mathcal F_m to be a Galois G-covering in the sense of \citeBL. If in addition A is a dualizing category and mod A has finite global dimension 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), whenever A is any finite dimensional k-algebra over a field k.

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