Proof of the representation-finite result avoiding structure theory

Determine whether the Cartan determinant theorem for representation-finite algebras can be proved without using the structure theory of representation-finite algebras developed by Bautista, Gabriel, Roiter, and Salmeron.

Background

The proofs of the paper’s main results rely on the structure theory of representation-finite algebras, particularly the characterization of standard algebras via Auslander–Reiten quivers and mesh categories. The author explicitly leaves unresolved whether an alternative proof can avoid this theory.