On the form of the finite-dimensional projective representations of an infinite abelian group
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- by N. B. Backhouse PDF
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Abstract:
If the locally compact abelian group $G$ has a finite-dimensional unitary irreducible projective representation with factor system $\omega$ (i.e. $G$ has an $\omega$-rep), then a subgroup $G(\omega )$ is defined which fulfils three roles. First, the square-root of the index of $G(\omega )$ in $G$ is the dimension of every $\omega$-rep. Secondly, the $\omega$-reps of $G$ can be labelled by the dual group of $G(\omega )$, up to unitary equivalence. Thirdly, the essential projective form of an $\omega$-rep is determined by a unique projective representation of the finite group $G/G(\omega )$.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 294-298
- MSC: Primary 22D12
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318393-6
- MathSciNet review: 0318393