Ringel duality and Auslander-Dlab-Ringel algebras

TL;DR

This paper introduces a new class of quasi-hereditary algebras, including ADR algebras, showing their invariance under Ringel duality and explicitly determining their duals, thus generalizing recent results.

Contribution

It defines a new class of algebras preserved under Ringel duality and explicitly describes the duals of ADR algebras, extending previous work in the field.

Findings

The new class of algebras is closed under Ringel duality.

Explicit description of the Ringel duals of ADR algebras.

Provides a general framework that includes recent specific results.

Abstract

We introduce a new class of quasi-hereditary algebras, containing in particular the Auslander-Dlab-Ringel (ADR) algebras. We show that this new class of algebras is preserved under Ringel duality, which determines in particular explicitly the Ringel dual of any ADR algebra. As a special case of our theory, it follows that, under very restrictive conditions, an ADR algebra is Ringel dual to another one. The latter provides an alternative proof for a recent result of Conde and Erdmann, and places it in a more general setting.