DMCA
Operator Algebras and Poisson Manifolds Associated to Groupoids (2001)
by
N. P. Landsman
| Citations: | 9 - 3 self |
BibTeX
@MISC{Landsman01operatoralgebras,
author = {N. P. Landsman},
title = {Operator Algebras and Poisson Manifolds Associated to Groupoids},
year = {2001}
}
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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 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 C # (G), and G are functorial between the categories in question. It follows that these maps preserve Morita equivalence.
