Functoriality and Morita Equivalence of Operator Algebras and Poisson Manifolds Associated to Groupoids *
نویسنده
چکیده
It is well known that a measured groupoid G defines a von Neu-mann 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) are functorial with respect to suitable categories. In these categories Morita equivalence is isomorphism of objects, so that these maps preserve Morita equivalence.
منابع مشابه
Functoriality and Morita Equivalence of C * -algebras and Poisson Manifolds Associated to Lie Groupoids
It is well known 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 → C * (G) and G → A * (G) are functorial with respect to suitably defined categories. The arrows (Hom-spaces) between Lie groupoids are taken to be isomorphism classes of regular bibundles (Hilsum–Skandalis maps), composed by a canonical bibundle tensor p...
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