Functoriality and Morita equivalence of operator algebras and Poisson manifolds associated to groupoids
Abstract
Description
It is well known that a measured groupoid G defines a von Neumann algebra W*(G), and that a Lie groupoid G canonically defines both a C*-algebra C*(G) and a Poisson manifold A*(G). We show that the maps G -> W*(G), G -> C*(G) and G -> A*(G) are functorial with respect to suitable categories. In these categories Morita equivalence is isomorphism of objects, so that these maps preserve Morita equivalence.
23 pages, results on measured groupoids and von Neumann algebras added
23 pages, results on measured groupoids and von Neumann algebras added