Almost regular Poisson manifolds and their holonomy groupoids

Symplectic Groupoids and Poisson Manifolds

0. Introduction. A symplectic groupoid is a manifold T with a partially defined multiplication (satisfying certain axioms) and a compatible symplectic structure. The identity elements in T turn out to form a Poisson manifold To? and the correspondence between symplectic groupoids and Poisson manifolds is a natural extension of the one between Lie groups and Lie algebras. As with Lie groups, und...

Lie local subgroupoids and their holonomy and monodromy Lie groupoids

The notion of local equivalence relation on a topological space is generalized to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation of a monodromy principle on the extendability of local Lie morphisms.  2001 Elsevier Science B.V. All rights reserved. AMS classification: 58H05; 22A22; 18F20

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). 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 obj...

Strict Quantizations of Almost Poisson Manifolds

We show the existence of (non-Hermitian) strict quantization for every almost Poisson manifold.

Lie, symplectic and Poisson groupoids and their Lie algebroids