A characterization of right 4-Nakayama artin algebras

TL;DR

This paper characterizes right 4-Nakayama artin algebras by classifying modules, computing almost split sequences, and describing their quivers with relations, advancing understanding of their structure in representation theory.

Contribution

It provides a complete classification of modules and almost split sequences for right 4-Nakayama artin algebras, and characterizes these algebras via quivers with relations.

Findings

Classified all finitely generated indecomposable modules

Computed all almost split sequences over the algebra

Characterized right 4-Nakayama algebras by their quivers with relations

Abstract

We characterize right $4$-Nakayama artin algebras which appear naturally in the study of representation-finite artin algebras. For a right $4$-Nakayama artin algebra $\Lambda$, we classify all finitely generated indecomposable right $\Lambda$-modules and then we compute all almost split sequences over $\Lambda$. We also give a characterization of right $4$-Nakayama finite dimensional $K$-algebras in terms of their quivers with relations.