Coisotropic embeddings in Poisson manifolds
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- by A. S. Cattaneo and M. Zambon PDF
- Trans. Amer. Math. Soc. 361 (2009), 3721-3746 Request permission
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.References
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Additional Information
- A. S. Cattaneo
- Affiliation: Institut für Mathematik, Universität Zürich-Irchel, Winterthurerstr. 190, CH-8057 Zürich, Switzerland
- Email: alberto.cattaneo@math.unizh.ch
- M. Zambon
- Affiliation: Departamentos de Matematica Pura, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
- Email: mzambon@fc.up.pt
- Received by editor(s): May 25, 2007
- Published electronically: February 10, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 3721-3746
- MSC (2000): Primary 53D17; Secondary 53D55
- DOI: https://doi.org/10.1090/S0002-9947-09-04667-4
- MathSciNet review: 2491897