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On the integration of Poisson manifolds, Lie algebroids, and coisotropic submanifolds


Cattaneo, A S (2004). On the integration of Poisson manifolds, Lie algebroids, and coisotropic submanifolds. Letters in Mathematical Physics, 67(1):33-48.

Abstract

In recent years, methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this Letter it is shown that the latter method is actually related to (and may be derived from) a particular case of the former if one regards dual of Lie algebroids as special Poisson manifolds. The core of the proof is the fact, discussed in the second part of this Letter, that coisotropic submanifolds of a (twisted) Poisson manifold are in one-to-one correspondence with possibly singular Lagrangian subgroupoids of source-simply-connected (twisted) symplectic groupoids.

Abstract

In recent years, methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this Letter it is shown that the latter method is actually related to (and may be derived from) a particular case of the former if one regards dual of Lie algebroids as special Poisson manifolds. The core of the proof is the fact, discussed in the second part of this Letter, that coisotropic submanifolds of a (twisted) Poisson manifold are in one-to-one correspondence with possibly singular Lagrangian subgroupoids of source-simply-connected (twisted) symplectic groupoids.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:coisotropic submanifold - Lagrangian subgroupoid - Lie algebroid - Poisson manifold - symplectic groupoid - symplectic reduction - twisted Poisson manifold
Language:English
Date:2004
Deposited On:27 Jan 2010 12:32
Last Modified:05 Apr 2016 13:24
Publisher:Springer
ISSN:0377-9017
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1023/B:MATH.0000027690.76935.f3
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2063018
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1059.53064

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