We study two subgroups of the Picard group Pic(R-gr) 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(R-gr). We prove that in general these groups are not the same and show that they are related by an exact sequence of cohomology. © 1999 Elsevier Science B.V. All rights reserved.
Beattie, M., & Del Río, A. (1999). Graded equivalences and Picard groups. Journal of Pure and Applied Algebra, 141(2), 131–152. https://doi.org/10.1016/S0022-4049(98)00011-5