Linear Nakayama algebras which are higher Auslander algebras

2021/04/28 by Claus Michael Ringel, Ringel, Claus Michael · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2104.13806

openalex publication_date 2021/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• The resolution quiver of Nakayama algebras which are minimal Auslander-Gorenstein

Related

• On the classification of higher Auslander algebras for Nakayama algebras
• Nakayama Algebras which are Higher Auslander Algebras
• Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories
• The resolution quiver of Nakayama algebras which are minimal Auslander-Gorenstein
• An Auslander-Buchsbaum formula for higher Auslander algebras and applications