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

CHAIO, CLAUDIA; A. GONZ\'ALEZ CHAIO, I. PRATTI AND M. J. SOUTO SALORIO.

JOURNAL OF PURE AND APPLIED ALGEBRA

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2024 vol. 228

0022-4049

Let A be an additive k-category and {C}_{equiv m}(A) be the category of $m-$periodic complexes. For any integer $m>1$, we study conditions under which the compression functor ${mathcal F}_m: C^{b}(mathcal{A}) ightarrow mathbf{C}_{equiv m}(mathcal{A})$ 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 cite{BL}. If in addition $A$ is a dualizing category and $mbox{mod}, A$ has finite global dimension then $mathbf{C}_{equiv m}(mathcal{A})$ 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 $C_{equiv m}(mbox{proj}, A)$. Furthermore, we study the behavior of sectional paths in $C_{equiv m}(mbox{proj}, A)$, when $A$ is a finite dimensional algebra over a field $k$.