Schur’s theory for partial projective representations

Abstract

This article focuses on those aspects about partial actions of groups which are related to Schur’s theory on projective representations. It provides an exhaustive description of the partial Schur multiplier, and this result is achieved by introducing the concept of a second partial cohomology group relative to an ideal, together with an appropriate analogue of a central extension. In addition, the new framework is proved to be consistent with the earlier notion of cohomology over partial modules.