The Gorenstein projective modules for the Nakayama algebras. I

TL;DR

This paper characterizes the Gorenstein projective modules over Nakayama algebras, introducing a resolution quiver that facilitates classification and Gorenstein property determination.

Contribution

It introduces the resolution quiver for Nakayama algebras, providing a new tool to classify Gorenstein projective modules and determine Gorenstein properties efficiently.

Findings

Resolution quiver enables quick classification of Gorenstein projective modules.

Algorithm determines if the algebra is Gorenstein or CM-free.

Provides structural insights into Gorenstein modules for Nakayama algebras.

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.