## 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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