Homological dimensions for endomorphism algebras of Gorenstein projective modules

Abstract

Let A be a CM-finite Artin algebra with a Gorenstein-Auslander generator E, M be a Gorenstein projective A-module and B = End_AM. We give an upper bound for the finitistic dimension of B in terms of homological data of M. Furthermore, if A is n-Gorenstein for 2 ⩽ n < ∞, then we show the global dimension of B is less than or equal to n plus the B-projective dimension of Hom_A(M, E). As an application, the global dimension of End_AE is less than or equal to n.