A universal property for groupoid C*-algebras. I

Abstract

We describe representations of groupoid C*-algebras on Hilbert modules over arbitrary C*-algebras by a universal property. For Hilbert space representations, our universal property is equivalent to Renault's Integration-Disintegration Theorem. For a locally compact group, it is related to the automatic continuity of measurable group representations. It implies known descriptions of groupoid C*-algebras as crossed products for étale groupoids and transformation groupoids of group actions on spaces.

Final version accepted for publication at Proc. London Math. Soc

References in corpus (2)

• Inverse semigroup actions on groupoids
• Fell bundles over inverse semigroups and twisted etale groupoids

Cited by in corpus (3)

• Banach algebras associated to twisted étale groupoids: inverse semigroup disintegration and representations on $L^p$-spaces
• Topological freeness for $C^{\ast }$-correspondences
• Locally free actions of groupoids and proper topological correspondences