GROUPOIDS AND THE INTEGRATION OF LIE ALGEBROIDS

By Victor Nistor. 2000

70 citations recorded by the source corpus.

We show that a Lie algebroid on a stratified manifold is integrable if, and only if, its restriction to each strata is integrable. These results allow us to construct a large class of algebras of pseudodifferential operators.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f6edbd7fc76f00cd718dbf88faa7befbc2ede5d9

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In Algebra and Number Theory

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Citations in the corpus

Integrability of Lie brackets (2001, methodology): “As explained in [22], such Γ’s arise naturally in the analysis on manifolds with corners as algebras of vector fields with a certain behavior on the faces of M .”
Lectures on integrability of Lie brackets (2006, unknown): “Other fundamental examples were discovered over many years by different authors, such as Élie Cartan’s infinite continuous groups (Singer and Sternberg, [56]), the integrability of infinitesimal actions on manifolds (Palais, [50], Moerdijk and Mrčun [47]), abstract Atiyah sequences and transitive Li”
HOLONOMY GROUPOIDS OF SINGULAR FOLIATIONS (2001, background): “Nistor has studied integrability of Lie algebroids over stratified manifolds [21].”
The holonomy groupoid of a singular foliation (2006, background): “(For an account of the exponential map, as well as this di¤eomorphism see [19].”
Analysis of geometric operators on open manifolds: A groupoid approach (2000, methodology): “To integrate TM , we shall use the methods of [29].”
Symplectic groupoids of log symplectic manifolds (2012, methodology): “The second method is a gluing construction, inspired by the work of Nistor [20].”