TY - JOUR
AU - Zhang, Yi
AB - Let A be an Artin algebra and let Gprj-Λ denote the class of all the finitely generated Gorenstein projective Λ-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a certain subcategory of the monomorphism category S(Gprj-Λ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\cal{S}}(\text{Gprj-}\Lambda)$$\end{document} containing boundary vertices. We describe the shape of such components. It is shown that certain components are linked to the orbits of an auto-equivalence on the stable category Gprj-Λ. In particular, for the finite components, we show that under certain mild conditions, their cardinalities are divisible by 3. We see that this three-periodicity phenomenon reoccurs several times in the paper.
TI - The stable Auslander-Reiten components of certain monomorphism categories
JF - Science China Mathematics
DO - 10.1007/s11425-022-2095-1
DA - 2024-03-01
UR - https://www.deepdyve.com/lp/springer-journals/the-stable-auslander-reiten-components-of-certain-monomorphism-F1nXBFiP7Y
SP - 505
EP - 526
VL - 67
IS - 3
DP - DeepDyve
ER -