On $n$-hereditary algebras and $n$-slice algebras

Jin Yun Guo, Yanping Hu

Published 2022-04-14Version 1

In this paper we show that $n$-slice algebras are exactly $n$-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 pair and they share the Auslander-Reiten quiver for their higher preprojective components.