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Continuous trace groupoid \(C^*\)-algebras. (English) Zbl 0782.46048

Let \(G\) be a locally compact groupoid with a Haar system \(\{\lambda^ u\}_{u\in G_ 0}\). The main result in this paper is that if \(G\) is a second countable, principal groupoid, then \(C^*(G,\lambda)\), the \(C^*\)-algebra of \(G\), has continuous trace if and only if \(G\) is proper.

MSC:

46L05 General theory of \(C^*\)-algebras
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