Functoriality and Morita equivalence of operator algebras and Poisson manifolds associated to groupoids

Details Functoriality and Morita equivalence of operator algebras and Poisson manifolds associated to groupoids Functoriality and Morita equivalence of operator algebras and Poisson manifolds associated to groupoids

2000-08-25

arxiv.org/abs/math-ph/0008036v3

Physics

Mathematical Physics

23 pages, results on measured groupoids and von Neumann algebras added

Scientific paper

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.

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