From Gorenstein derived equivalences to stable functors of Gorenstein projective modules

TL;DR

This paper explores the relationship between Gorenstein derived equivalences and stable functors of Gorenstein projective modules, establishing conditions under which these functors induce equivalences between certain module categories.

Contribution

It demonstrates that Gorenstein derived equivalences between CM-finite algebras induce stable functors, which become equivalences when the algebras are Gorenstein.

Findings

Gorenstein derived equivalences induce stable functors between module categories.

Stable functors become equivalences for Gorenstein algebras.

Connects Gorenstein derived equivalences with stable module theory.

Abstract

In the paper, we mainly connect the Gorenstein derived equivalence and stable functors of Gorenstein projective modules. Specially, we prove that a Gorenstein derived equivalence between CM-finite algebras A and B can induce a stable functor between the factor categories A-mod/A-Gproj and B-mod\B-Gproj. Furthermore, the above stable functor is an equivalence when A and B are Gorenstein.