Inducing primitive ideals

Echterhoff, Siegfried; Williams, Dana

doi:10.1090/S0002-9947-08-04499-1

Inducing primitive ideals
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by Siegfried Echterhoff and Dana P. Williams PDF

Trans. Amer. Math. Soc. 360 (2008), 6113-6129 Request permission

Abstract:

We study conditions on a $C^*$-dynamical system $(A,G,\alpha )$ under which induction of primitive ideals (resp. irreducible representations) from stabilizers for the action of $G$ on the primitive ideal space $\mathrm {Prim}(A)$ give primitive ideals (resp. irreducible representations) of the crossed product ${A \rtimes _\alpha G}$. The results build on earlier results of Sauvageot and others and will correct a (possibly overly optimistic) statement of the first author. In an appendix, the first author takes the opportunity to fill a gap in the proof of an earlier result.

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