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

TL;DR

This paper characterizes acyclic n-slice algebras as a special class of n-hereditary algebras with Koszul properties and explores their associated triangulated categories and finite type pairs.

Contribution

It establishes a precise equivalence between acyclic n-slice and n-hereditary algebras with Koszul preprojective algebras, and analyzes their triangulated categories and finite type pairs.

Findings

Acyclic n-slice algebras are exactly acyclic n-hereditary algebras with (q+1,n+1)-Koszul preprojective algebras.

Higher slice algebras of finite type appear in pairs sharing the same Auslander-Reiten quiver.

The paper lists the triangulated categories arising from algebra constructions related to 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 components.