Partial projective representations and partial actions II

This paper is a continuation of Dokuchaev and Novikov (2010) [8], . The interaction between partial projective representations and twisted partial actions of groups considered in Dokuchaev and Novikov (2010) [8] is treated now in a categorical language. In the case of a finite group G, a structural result on the domains of factor sets of partial projective representations of G is obtained in terms of elementary partial actions. For arbitrary G we study the component pM′(G) of totally-defined factor sets in the partial Schur multiplier pM(G) using the structure of Exel’s semigroup. A complete characterization of the elements of pM′(G) is obtained for algebraically closed fields.