ON HOMOTOPY CATEGORIES OF GORENSTEIN MODULES: COMPACT GENERATION AND DIMENSIONS

Let A be a virtually Gorenstein algebra of finite CM-type. We establish a duality between the subcategory of compact objects in the homotopy category of Gorenstein projective left A-modules and the bounded Gorenstein derived category of finitely generated right A-modules. Let R be a two-sided noetherian ring such that the subcategory of Gorenstein flat modules R-GF is closed under direct products. We show that the inclusion K(R-GF) -> K(R-Mod) of homotopy categories admits a right adjoint. We introduce the notion of Gorenstein representation dimension for an algebra of finite CM-type, and give a lower bound by the dimension of its bounded Gorenstein derived category.