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

math-ph/0008036Aug 25, 200023 pages, results on measured groupoids and von Neumann algebras added

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

N. P. Landsman

Mathematical Physics Operator Algebras Symplectic Geometry

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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The paper addresses: Functoriality and Morita equivalence of operator algebras and Poisson manifolds associated to groupoids.
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).

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