Abstract
Realizations of a Poisson manifold by symplectic groupoids, if they exist, are a very important tool in both the geometry and the quantization of the Poisson manifolds. This theory can be seen as starting with the papers of Karasev and Maslov [KM1,2], and it was developed by A. Weinstein, and then by P. Dazord, G. Hector and others [We5–10], [CDW], [DH], [MW], [AD1,2], [AC2], etc. The problem of finding such realizations can be seen as a generalization of the famous Lie’s third theorem in the theory of the Lie groups, and we shall motivate it precisely from this viewpoint.
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© 1994 Springer Basel AG
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Vaisman, I. (1994). Realizations of Poisson Manifolds by Symplectic Groupoids. In: Lectures on the Geometry of Poisson Manifolds. Progress in Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8495-2_10
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DOI: https://doi.org/10.1007/978-3-0348-8495-2_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9649-8
Online ISBN: 978-3-0348-8495-2
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