A universal property for groupoid C-*-algebras.

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 etale groupoids and transformation groupoids of group actions on spaces.