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

N. P. Landsman
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Abstract

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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BibTeXRIS

N. P. Landsman. 2000-11-29. Functoriality and Morita equivalence of operator algebras and Poisson manifolds associated to groupoids. https://arxiv.org/abs/math-ph/0008036

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