Invariants and Gorenstein projective modules

TL;DR

This paper explores invariants of Gorenstein projective modules, introduces the Gorenstein rigidity dimension, and demonstrates its invariance under various algebraic equivalences, providing bounds for different algebra classes.

Contribution

It introduces the Gorenstein rigidity dimension and proves its invariance under Morita, stable, and derived equivalences, advancing understanding of Gorenstein projective modules.

Findings

Gorenstein rigidity dimension is invariant under Morita and stable equivalences.

The Gorenstein rigidity dimension is also invariant under derived equivalences.

Bounds for Gorenstein rigidity dimension are established for various algebra classes.

Abstract

Invariants with respect to recollements of the stable category of Gorenstein projective A-modules over an algebra A and stable equivalences are investigated. Specifically, the Gorenstein rigidity dimension is introduced. It is shown that the Gorenstein rigidity dimension is invariant with respect to both Morita equivalences and the stable equivalences of Gorenstein projective modules. As a consequence, the Gorenstein rigidity dimension is shown the invariant of derived equivalences. The Gorenstein rigidity dimension is compared along the recollements of the stable category of Gorenstein projective modules. Moreover, the bounds of Gorenstein rigidity dimension is given for several classes of algebras, respectively.