Primitive ideals of $C^{\ast }$-algebras associated with transformation groups
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- by Elliot C. Gootman PDF
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Abstract:
We extend results of E. G. Effros and F. Hahn concerning their conjecture that if $(G,Z)$ is a second countable locally compact transformation group, with $G$ amenable, then every primitive ideal of the associated ${C^ \ast }$-algebra arises as the kernel of an irreducible representation induced from an isotropy subgroup. The conjecture is verified if all isotropy subgroups lie in the center of $G$ and either (a) the restriction of each unitary representation of $G$ to some open subgroup contains a one-dimensional subrepresentation, or (b) $G$ has an open abelian subgroup and orbit closures in $Z$ are compact and minimal.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 170 (1972), 97-108
- MSC: Primary 22D25; Secondary 46L05
- DOI: https://doi.org/10.1090/S0002-9947-1972-0302818-X
- MathSciNet review: 0302818