A Note on Gorenstein Projective Conjecture II

TL;DR

This paper proves the symmetry of the Gorenstein projective conjecture and confirms its validity for CM-finite algebras, clarifying conditions under which cohomology vanishing cannot be simplified.

Contribution

It establishes the symmetry of the Gorenstein projective conjecture and verifies its truth for CM-finite algebras, advancing understanding in Gorenstein homological algebra.

Findings

Gorenstein projective conjecture is symmetric

Cohomology vanishing condition cannot be generally reduced

Conjecture holds for CM-finite algebras

Abstract

In this paper, we prove that Gorenstein projective conjecture is left and right symmetric and the co-homology vanishing condition can not be reduced in general. Moreover, the Gorenstein projective conjecture is proved to be true for CM-finite algebras.