Representation dimension of artin algebras

Abstract

Auslander has shown that an algebra is of finite representation type, that is, it admits only finitely many indecomposable modules up to isomorphism, if and only if its representation dimension is at most 2. We will give a proof of this fact in Section 1 as Corollary 1.9. This led Auslander to the expectation, “that this notion gives a reasonable way of measuring how far an artin algebra is from being of finite representation type.” [1, III.5, lines 2, 3]