Journal of the Mathematical Society of Japan

Groupoids and the integration of Lie algebroids

Victor NISTOR

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Abstract

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. They are also relevant for the definition of the graph of certain singular foliations of manifolds with corners and the construction of natural algebras of pseudodifferential operators on a given complex algebraic variety.

Article information

Source
J. Math. Soc. Japan, Volume 52, Number 4 (2000), 847-868.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107113

Digital Object Identifier
doi:10.2969/jmsj/05240847

Mathematical Reviews number (MathSciNet)
MR1774632

Zentralblatt MATH identifier
0965.58023

Subjects
Primary: 58H05: Pseudogroups and differentiable groupoids [See also 22A22, 22E65]
Secondary: 58J40: Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx] 46L87: Noncommutative differential geometry [See also 58B32, 58B34, 58J22]

Keywords
Groupoid differential groupoid pseudodifferential operator Lie algebroid manifold with corners non-commutative geometry

Citation

NISTOR, Victor. Groupoids and the integration of Lie algebroids. J. Math. Soc. Japan 52 (2000), no. 4, 847--868. doi:10.2969/jmsj/05240847. https://projecteuclid.org/euclid.jmsj/1213107113


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