Partial projective representations and partial actions II

Abstract

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 p M ′ ( G ) of totally-defined factor sets in the partial Schur multiplier p M ( G ) using the structure of Exel’s semigroup. A complete characterization of the elements of p M ′ ( G ) is obtained for algebraically closed fields.