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

 

Projective representations of abelian groups


Authors: N. B. Backhouse and C. J. Bradley
Journal: Proc. Amer. Math. Soc. 36 (1972), 260-266
MSC: Primary 22D12
MathSciNet review: 0308329
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Abstract: Let $ \omega $ be a factor system for the locally compact abelian group G. Then we show that the finite-dimensional unitary irreducible projective representations of G, having factor system $ \omega $, possess a common dimension $ d(\omega )$. Using a characterisation of $ d(\omega )$ as the index in G of a maximal subgroup on which $ \omega $ is symmetric we derive a formula for $ d(\omega )$ in the case that G is discrete and finitely generated.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0308329-5
PII: S 0002-9939(1972)0308329-5
Keywords: Locally compact abelian group, projective representation, factor system, Kronecker product, abelian group, finitely generated abelian group
Article copyright: © Copyright 1972 American Mathematical Society