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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 28th 2015
   • (edited May 28th 2015)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded to _[[Poisson manifold]]_ a subsection * _[Presymplectic manifolds and infinitesimal quantomorphisms](http://ncatlab.org/nlab/show/Poisson+manifold#PresymplecticManifolds)_ which states the form of the Poisson bracket on presymplectic manifolds and then discusses how this is isomorphic as a Lie algebra to the infinitesimal quantomorphisms, the infinitesimal symmetries of any prequantization of the presymplectic manifold. I have written that as one subsection for the exposition at _[[geometry of physics -- prequantum geometry]]_, but I suppose it serves well to have it right there in the entry on Poisson brackets itsef, too.

   added to Poisson manifold a subsection

   • Presymplectic manifolds and infinitesimal quantomorphisms

   which states the form of the Poisson bracket on presymplectic manifolds and then discusses how this is isomorphic as a Lie algebra to the infinitesimal quantomorphisms, the infinitesimal symmetries of any prequantization of the presymplectic manifold.

   I have written that as one subsection for the exposition at geometry of physics – prequantum geometry, but I suppose it serves well to have it right there in the entry on Poisson brackets itsef, too.

2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMar 20th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: The original reference is * [[André Lichnerowicz]], _Les variétés de Poisson et leurs algèbres de Lie associées_, Journal of Differential Geometry 12:2 (1977), 253–300. [doi](http://dx.doi.org/10.4310/jdg/1214433987). <a href="https://ncatlab.org/nlab/revision/diff/Poisson+manifold/36">diff</a>, <a href="https://ncatlab.org/nlab/revision/Poisson+manifold/36">v36</a>, <a href="https://ncatlab.org/nlab/show/Poisson+manifold">current</a>

   Added:

   The original reference is

   • André Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, Journal of Differential Geometry 12:2 (1977), 253–300. doi.

   diff, v36, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 4th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Alan Weinstein]], *The local structure of Poisson manifolds*, J. Differential Geom. **18** 3 (1983) 523-557 &lbrack;[doi:10.4310/jdg/1214437787](https://projecteuclid.org/journals/journal-of-differential-geometry/volume-18/issue-3/The-local-structure-of-Poisson-manifolds/10.4310/jdg/1214437787.full)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Poisson+manifold/39">diff</a>, <a href="https://ncatlab.org/nlab/revision/Poisson+manifold/39">v39</a>, <a href="https://ncatlab.org/nlab/show/Poisson+manifold">current</a>

   added pointer to:

   • Alan Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 3 (1983) 523-557 [doi:10.4310/jdg/1214437787]

   diff, v39, current