Quasi-hereditary covers of higher zigzag-algebras

TL;DR

This paper introduces quasi-hereditary covers for higher zigzag algebras, demonstrating their Koszul properties and computing their duals, thus advancing the understanding of their algebraic structure.

Contribution

It defines and studies quasi-hereditary covers of higher zigzag algebras, establishing their Koszul properties and explicitly computing their duals.

Findings

Higher zigzag algebras are Koszul in multiple senses

Quasi-hereditary covers satisfy standard Koszul properties

The $ ext{Δ}$-Koszul dual is explicitly computed as a quiver with relations

Abstract

The aim of this paper is to define and study some quasi-hereditary covers for higher zigzag algebras. We will show how these algebras satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and Koszul with respect to the standard module $\Delta$, according with the definition given in \cite{Madsen1}. This last property gives rise to a well defined duality and the $\Delta$-Koszul dual will be computed as the path algebra of a quiver with relations.