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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 a theorem of Fell


Author: Robert C. Busby
Journal: Proc. Amer. Math. Soc. 30 (1971), 133-140
MSC: Primary 46.80; Secondary 22.00
MathSciNet review: 0283583
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Abstract: Fell has proved that the process of inducing representations of a locally compact group from representations of closed subgroups is a continuous process if topologies are defined on the spaces of representations in the right way. As a corollary he shows that inducing preserves weak containment. This paper generalizes Fell's results to twisted group algebras. These algebras generalize the idea of the group algebra of a group extension, and the concept of induced representation extends in a natural way. We show that Fell's results will hold if the ``cocycle pair'' defining the twisting of the algebra is sufficiently continuous.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0283583-6
PII: S 0002-9939(1971)0283583-6
Keywords: Twisted group algebra, induced representation, inner hullkernel topology, quotient topology, weak containment
Article copyright: © Copyright 1971 American Mathematical Society