Partial representations and their domains

Abstract

We study the structure of the partially or\-dered set of the elementary domains of partial (linear or projective) representations of groups. This provides an important information on the lattice of all domains. Some of these results are obtained through structural facts on the ideals of the semigroup $\mathcal{S} _3(G)$, a quotient of Exel's semigroup $\mathcal{S} (G)$, which plays a crucial role in the theory of partial projective representations. We also fill a gap in the proof of an earlier result on the structure of partial group representations.