Right n-Nakayama algebras and their representations

Abstract

In this paper we study right $n$-Nakayama algebras. Right $n$-Nakayama algebras appear naturally in the study of representation-finite algebras. We show that an artin algebra $\Lambda$ is representation-finite if and only if $\Lambda$ is right $n$-Nakayama for some positive integer $n$. We classify hereditary right $n$-Nakayama algebras. We also define right $n$-coNakayama algebras and show that an artin algebra $\Lambda$ is right $n$-coNakayama if and only if $\Lambda$ is left $n$-Nakayama. We then study right $2$-Nakayama algebras. We show how to compute all the indecomposable modules and almost split sequences over a right $2$-Nakayama algebra. We end by classifying finite dimensional right $2$-Nakayama algebras in terms of their quivers with relations.