The Gorenstein projective modules for the Nakayama algebras. I

Abstract

The aim of this note is to outline the structure of the category of the Gorenstein projective modules for a Nakayama algebra. We are going to introduce the resolution quiver of such an algebra. It provides a fast algorithm in order to obtain the Gorenstein projective modules and to decide whether the algebra is a Gorenstein algebra or not, and whether it is CM-free or not.