We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras. The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained using ray-categories. As applications we include a proof of a sharper version of the second Brauer–Thrall conjecture and of the fact that there are no gaps in the lengths of the indecomposables.

On representation-finite algebras and beyond

Klaus Bongartz

Abstract