Inducing Primitive Ideals

Abstract

We study conditions on a $C^{\ast }$-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 $\Prim(A)$ give primitive ideals (resp. irreducible representations) of the crossed product $A{⋊}_{\alpha }G$. The results build on earlier results of Sauvageot and others, and will correct a (possibly overly optimistic) statement of the first author.

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