Invariants and Gorenstein projective modules

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.