Inducing primitive ideals

Abstract

We study conditions on a C ∗ -dynamical system (A,G,�) under which induction of primitive ideals (resp. irreducible representations) from stabilizers for the action of G on the primitive ideal space Prim(A) give primitive ideals (resp. irreducible representations) of the crossed product A ⋊� G. The results build on earlier results of Sauvageot (17) and others, and will correct a (possibly overly optimistic) statement of the first author in (5). In an appendix, the first author takes the opportunity to fill a gap in the proof of another result in (5).