Primitive ideals of 𝐶*-algebras associated with transformation groups

Gootman, Elliot C.

doi:10.1090/S0002-9947-1972-0302818-X

Primitive ideals of $C^{\ast }$-algebras associated with transformation groups
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by Elliot C. Gootman PDF

Trans. Amer. Math. Soc. 170 (1972), 97-108 Request permission

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.

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