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.