On n-hereditary algebras and n-slice algebras

Abstract

In this paper we show that acyclic n-slice algebras are exactly acyclic n-hereditary algebras whose (n+1)-preprojective algebras are (q+1,n+1)-Koszul. We also list the equivalent triangulated categories arising from the algebra constructions related to an n-slice algebra. We show that higher slice algebras of finite type appear in pairs and they share the Auslander-Reiten quiver for their higher-preprojective modules.