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Coisotropic embeddings in Poisson manifolds


Cattaneo, A S; Zambon, M (2009). Coisotropic embeddings in Poisson manifolds. Transactions of the American Mathematical Society, 361(7):3721-3746.

Abstract

We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition, already considered by Calvo and Falceto (2004), sits coisotropically inside some larger cosymplectic submanifold, which is naturally endowed with a Poisson structure. Then we give conditions under which a Dirac manifold can be embedded coisotropically in a Poisson manifold, extending a classical theorem of Gotay.

Abstract

We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition, already considered by Calvo and Falceto (2004), sits coisotropically inside some larger cosymplectic submanifold, which is naturally endowed with a Poisson structure. Then we give conditions under which a Dirac manifold can be embedded coisotropically in a Poisson manifold, extending a classical theorem of Gotay.

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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
Language:English
Date:2009
Deposited On:13 Oct 2009 13:40
Last Modified:05 Apr 2016 13:22
Publisher:American Mathematical Society
ISSN:0002-9947
Additional Information:First published in Trans. Amer. Math. Soc. 361(7):3721-3746, 2009, published by the American Mathematical Society.
Publisher DOI:https://doi.org/10.1090/S0002-9947-09-04667-4
Related URLs:http://arxiv.org/abs/math/0611480
http://www.ams.org/mathscinet-getitem?mr=2491897

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