Linear Nakayama algebras which are higher Auslander algebras

Abstract

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

Keywords:

• Higher Auslander algebra
• Nakayama algebra

2020 Mathematics Subject Classification:

• Primary: 16G10
• Secondary: 16G20
• 16G70
• 16E05
• 16E10
• 16E65

Acknowledgments

The author thanks the referee for a very careful reading of two preliminary versions, pointing out a huge number of inaccuracies and misprints. In fact, on the basis of the first comments, the paper was completely rewritten.