Operator Algebras and Poisson Manifolds Associated to Groupoids
نویسنده
چکیده
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 construct suitable categories of measured groupoids, Lie groupoids, von Neumann algebras, C∗-algebras, and Poisson manifolds, with the feature that in each case Morita equivalence comes down to isomorphism of objects. Subsequently, we show that the maps G → W ∗(G), G → C∗(G), and G → A∗(G) are functorial between the categories in question. It follows that these maps preserve Morita equivalence.
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