McKay quivers and absolute n-complete algebras

In this paper, we show that the McKay quiver of a finite subgroup of a general linear group is a regular covering of the McKay quiver of its intersection with the special linear group. Using this and our results on “returning arrows” in McKay quiver, we give an algorithm to construct the McKay quiver of a finite abelian group. Using this construction, we show how the cone and cylinder of an (n?1)-Auslander absolute n-complete algebra are truncated from the McKay quivers of abelian groups.