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N. B. BACKHOUSEAbstract. If the locally compact abelian group G has a finite-dimensional unitary irreducible projective representation withfactor system co (i.e. G has an a>-rep), then a subgroup G(co) isdefined which fulfils three roles. First, the square-root of the indexof G(u)) in G is the dimension of every co-rep. Secondly, the co-repsof G can be labelled by the dual group of G(co), up to unitaryequivalence. Thirdly, the essential projective form of an co-rep isdetermined by a unique projective representation of the finitegroup G/G(co).

On the form of the finite-dimensional projective representations of an infinite abelian group