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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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


Author: N. B. Backhouse
Journal: Proc. Amer. Math. Soc. 41 (1973), 294-298
MSC: Primary 22D12
MathSciNet review: 0318393
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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 )$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0318393-6
PII: S 0002-9939(1973)0318393-6
Keywords: Locally compact abelian group, projective representation, factor system, $ \omega $-regular class, $ \omega $-symmetric subgroup
Article copyright: © Copyright 1973 American Mathematical Society