A Smashing Subcategory of the Homotopy Category of Gorenstein Projective Modules

Abstract

Let A be an artin algebra of finite CM-type. In this paper, we show that if A is virtually Gorenstein, then the homotopy category of Gorenstein projective A-modules, denote K(A-GP), is always compactly generated. Based on this result, it will be proved that the homotopy category of projective A-modules, denote K(A-P), is a smashing subcategory of K(A-GP) and the corresponding Verdier quotient is also compactly generated. Furthermore, it turns out that the inclusion functor i : K(A-P) → K(A-GP) induces a recollement of K(A-GP).