On the classification of higher Auslander algebras for Nakayama algebras

TL;DR

This paper improves bounds on the dominant dimension of Nakayama algebras, classifies certain higher Auslander algebras among them, and extends known inequalities related to their global dimension.

Contribution

It provides new bounds for dominant dimension and a classification of higher Auslander Nakayama algebras with large global dimension.

Findings

New bounds for dominant dimension of Nakayama algebras

Classification of higher Auslander Nakayama algebras with global dimension ≥ n

Extended inequalities for global dimension of Nakayama algebras

Abstract

We give new improved bounds for the dominant dimension of Nakayama algebras and use those bounds to give a classification of Nakayama algebras with $n$ simple modules that are higher Auslander algebras with global dimension at least $n$. The classification is then used to extend the results on the inequality for the global dimension of Nakayama algebras obtained in \cite{MM}.