Ringel duality for certain strongly quasi-hereditary algebras

TL;DR

This paper introduces a new class of quasi-hereditary algebras over monomial algebras and provides a uniform formula for their Ringel duals, extending known duality results to various algebra families.

Contribution

It presents a general formula for Ringel duals of certain quasi-hereditary algebras, unifying several special cases and extending duality theory.

Findings

Derived a uniform Ringel duality formula for new algebra class

Established duality results for algebras from geometric configurations

Recovered known self-duality of Nakayama algebra Auslander algebras

Abstract

We introduce quasi-hereditary endomorphism algebras defined over a new class of finite dimensional monomial algebras with a special ideal structure. The main result is a uniform formula describing the Ringel duals of these quasi-hereditary algebras. As special cases, we obtain a Ringel-duality formula for a family of strongly quasi-hereditary algebras arising from a type A configuration of projective lines in a rational, projective surface as recently introduced by Hille and Ploog, for certain Auslander-Dlab-Ringel algebras, and for Eiriksson and Sauter's nilpotent quiver algebras when the quiver has no sinks and no sources. We also recover Tan's result that the Auslander algebras of self-injective Nakayama algebras are Ringel self-dual.