ℤQ type constructions in higher representation theory

Abstract

It is classical that certain truncations of the translation quiver Z Q appear in the Auslander-Reiten quiver. The stable n-translation quiver Z | n − 1 Q is introduced as a generalization of Z Q in studying higher representation theory. In this paper, we find conditions for a Hom-finite k-category to be realized as the bound path category of a convex full subquiver of a stable n-translation quiver. We show that the n-preinjective component and n-preprojective component of n-slice algebra are realized as the bound path categories of some truncations of Z | n − 1 Q o p . We also use Z | n − 1 Q o p to describe the νn -closure of Γ in the derived category.