Graded equivalences and Picard groups Original Research Article

We study two subgroups of the Picard group Pic(RGr) of a category of graded modules: the subgroup gr−Pic(R#PG) of classes of graded equivalences and the subgroup Pic(R#PG)G of classes of equivalences which commute with the suspensions in Pic(RGr). We prove that in general these groups are not the same and show that they are related by an exact sequence of cohomology.