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The primitive ideal space of twisted covariant systems with continuously varying stabilizers. (English) Zbl 0739.22006

The main purpose of the paper is to show that for any E-H regular twisted covariant system \((G,A,\tau)\) with continuously varying stabilizers the topology of the primitive ideal space of \(C^*(G,A,\tau)\), the twisted crossed product of \((G,A,\tau)\), can always be described in terms of subgroup representations via the Mackey machine. For this, very general constructions of subgroup algebras for covariant systems are given, and it is also shown that inducing and restricting representations of twisted covariant systems is continuous even when the subgroups are varying, which generalizes a similar result of Fell for locally compact groups.

MSC:

22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
22D30 Induced representations for locally compact groups
46L05 General theory of \(C^*\)-algebras
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References:

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