Ringel self-duality in infinite representation type

Determine what happens to hereditary algebras of infinite representation type under Ringel self-duality.

Background

The principal structural and classification results of the paper concern connected hereditary algebras of finite representation type, particularly path algebras of Dynkin quivers. The behavior of hereditary algebras of infinite representation type—such as those associated with non-Dynkin acyclic quivers—under Ringel self-duality is left unresolved.

References

What happens to hereditary algebras of infinite representation type under Ringel self-duality?

— Ringel self-duality of hereditary algebras via Auslander-Reiten theory  (2609.29942 - Cruz, 24 Sep 2026) in Section 4.3, “Open questions”