G-Gorenstein complexes

TL;DR

This paper introduces G-Gorenstein complexes within Gorenstein homological algebra, establishing their properties and equivalences with G-class modules, expanding the theoretical framework of Gorenstein complexes.

Contribution

It defines G-Gorenstein complexes and explores their equivalences with G-class modules, providing a new perspective in Gorenstein homological algebra.

Findings

G-Gorenstein complexes are introduced as a new concept.

Equivalences between G-Gorenstein complexes and G-class modules are established.

The paper extends the theoretical understanding of Gorenstein complexes.

Abstract

We present in the context of Gorenstein homological algebra the notion of a "G-Gorenstein complex" as the counterpart of the classical notion of a Gorenstein complex. In particular, we investigate equivalences between the category of G-Gorenstein complexes of fixed dimension and the G-class of modules.