Continuous-trace groupoid 𝐶*-algebras. III

Muhly, Paul; Renault, Jean; Williams, Dana

doi:10.1090/S0002-9947-96-01610-8

Continuous-trace groupoid $C^*$-algebras. III
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by Paul S. Muhly, Jean N. Renault and Dana P. Williams PDF

Trans. Amer. Math. Soc. 348 (1996), 3621-3641 Request permission

Abstract:

Suppose that $\mathcal {G}$ is a second countable locally compact groupoid with a Haar system and with abelian isotropy. We show that the groupoid $C^{*}$-algebra $C^*(\mathcal {G},\lambda )$ has continuous trace if and only if there is a Haar system for the isotropy groupoid $\mathcal {A}$ and the action of the quotient groupoid $\mathcal {G}/\mathcal {A}$ is proper on the unit space of $\mathcal {G}$.

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