Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] R. C. Busby and H. A. Smith, Representations of twisted group algebras, Trans. Amer. Math. Soc. 149 (1970), 503-537. MR 0264418 (41:9013)
  • [2] R. C. Busby and Irwin Schochetman, Compact induced representations, Canad. J. Math. (submitted). MR 0293418 (45:2495)
  • [3] R. C. Busby, I. Schochetman and H. A. Smith, Integral operators and the compactness of induced representations, Trans. Amer. Math. Soc. (submitted). MR 0295099 (45:4167)
  • [4] J. M. G. Fell, Weak containment and induced representations of groups, Canad. J. Math. 14 (1962), 237-268. MR 27 #242. MR 0150241 (27:242)
  • [5] -, Weak containment and induced representations of groups. II, Trans. Amer. Math. Soc. 110 (1964), 424-447. MR 28 #3114. MR 0159898 (28:3114)
  • [6] D. Montgomery and L. Zippin, Topological transformation groups, Interscience, New York, 1955. MR 17, 383. MR 0073104 (17:383b)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.80, 22.00

Retrieve articles in all journals with MSC: 46.80, 22.00

Additional Information

Keywords: Twisted group algebra, induced representation, inner hullkernel topology, quotient topology, weak containment
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society