Artin algebras of small representation bound

Abstract

This paper introduces a novel classification approach for representation-finite artin algebras in terms of the maximal length of their indecomposable modules of finite length, which we call the representation bound. To this end, we develop methods to compute almost split sequences and establish lower bounds for the lengths of the Auslander-Reiten translates of certain modules over artin algebras. We apply these techniques and results to explicitly classify artin algebras of representation bound $n$ for each positive integer $n \le 4.$