On a theorem of Fell
HTML articles powered by AMS MathViewer
- by Robert C. Busby PDF
- Proc. Amer. Math. Soc. 30 (1971), 133-140 Request permission
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
- Robert C. Busby and Harvey A. Smith, Representations of twisted group algebras, Trans. Amer. Math. Soc. 149 (1970), 503–537. MR 264418, DOI 10.1090/S0002-9947-1970-0264418-8
- Robert C. Busby and Irwin Schochetman, Compact induced representations, Canadian J. Math. 24 (1972), 5–16. MR 293418, DOI 10.4153/CJM-1972-002-3
- Robert C. Busby, Irwin Schochetman, and Harvey A. Smith, Integral operators and the compactness of induced representations, Trans. Amer. Math. Soc. 164 (1972), 461–477. MR 295099, DOI 10.1090/S0002-9947-1972-0295099-7
- J. M. G. Fell, Weak containment and induced representations of groups, Canadian J. Math. 14 (1962), 237–268. MR 150241, DOI 10.4153/CJM-1962-016-6
- J. M. G. Fell, Weak containment and induced representations of groups. II, Trans. Amer. Math. Soc. 110 (1964), 424–447. MR 159898, DOI 10.1090/S0002-9947-1964-0159898-X
- Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 133-140
- MSC: Primary 46.80; Secondary 22.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0283583-6
- MathSciNet review: 0283583