On the Form of the Finite-Dimensional Projective Representations of an Infinite Abelian Group

If the locally compact abelian group has a finite-dimensional unitary irreducible projective representation with factor system (i.e. has an -rep), then a subgroup <!-- MATH $G(\omega )$ --> is defined which fulfils three roles. First, the square-root of the index of <!-- MATH $G(\omega )$ --> in is the dimension of every -rep. Secondly, the -reps of can be labelled by the dual group of <!-- MATH $G(\omega )$ --> , up to unitary equivalence. Thirdly, the essential projective form of an -rep is determined by a unique projective representation of the finite group <!-- MATH $G/G(\omega )$ --> .