2022/04/25 by Rasool Hafezi, Yi Zhang, Hafezi, Rasool +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2204.11705
Let Λ be an Artin algebra and let \rmGprj-Λ denote the class of all 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(\rm Gprj-Λ) 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 \underline\rmGprj-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.