It is shown that every continuous unitary projective representation of a Polish group can be lifted to a Borel multiplier representation (i.e., to a representation “up to a Borel factor”) and that this, in turn, can be derived from a continuous (ordinary) representation of a Polish group obtained from a central topological extension of the group considered by the multiplicative group of all complex numbers of absolute value 1. One determines the factors of all Borel multiplier representations of the Bondi-Metzner-Sacks group when the subgroup of “supertranslations” is the additive group of a separable real Hilbert space.

Continuous unitary projective representations of Polish groups: The BMS-group

It is shown that there exist only two cohomology classes of Borel multipliers for the Bondi–Metzner–Sachs group B when the subgroup of ’’supertranslations’’ is the additive group of a separable real Hilbert space. This implies that all Borel multipliers for the universal covering group ? of B are coboundaries and so every continuous unitary projective representation of B can be obtained from a continuous unitary (ordinary) representation of ?.

P.J. McCarthy

Papers

Projective representations of the asymptotic symmetry group of general relativity