Linear Nakayama algebras which are higher Auslander algebras

TL;DR

This paper classifies monotone linear Nakayama algebras that are higher Auslander algebras, revealing that the classification depends on the parity of their global dimension.

Contribution

It provides a classification of monotone Nakayama algebras that are higher Auslander algebras based on the parity of their global dimension.

Findings

Classification depends on the parity of the global dimension.

Monotone Nakayama algebras can be characterized as higher Auslander algebras.

Explicit criteria for the classification are established.

Abstract

An artin algebra A is said to be a higher Auslander algebra provided the global dimension and the dominant dimension coincide. We say that a linear Nakayama algebra is monotone, provided its Kupisch series first increases, then decreases. We are going to classify the monotone Nakayama algebras which are higher Auslander algebras. Let us stress that the classification strongly depends on the parity of the global dimension of A.