Abstract
IfG is a second countable locally compact group acting continuously on a separableC *-algebraA, then every primitive ideal of the crossed productC * (G, A) is contained in an induced primitive ideal, and ifG is amenable, equality holds. Thus ifG is amenable and acts freely on Prim(A), the “generalized Effros-Hahn conjecture” holds: there is a canonical bijection between primitive ideals ofC * (G, A) andG-quasi-orbits in Prim(A). Applications to the “Mackey machine” for a non-regularly embedded normal subgroup of a locally compact group are discussed. The proof of the theorem is based on a “local cross-section” result together with Mackey's original methods.
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The authors were partially supported by National Science Foundation Research Grants
The first-named author would like to thank the Department of Mathematics, University of Pennsylvania, for its warm hospitality during his 1977–78 stay, during which time this research was conducted
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Gootman, E.C., Rosenberg, J. The structure of crossed productC *-algebras: A proof of the generalized Effros-Hahn conjecture. Invent Math 52, 283–298 (1979). https://doi.org/10.1007/BF01389885
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DOI: https://doi.org/10.1007/BF01389885