Ringel duality for certain strongly quasi-hereditary algebras

We study 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.