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

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 functor Fm:Cb(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 and modA 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(projA). Furthermore, we study the behavior of sectional paths in C≡m(projA), when A is a finite dimensional algebra over a field k.