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<full_title>WikiJournal of Science/Poisson manifold</full_title>
<abbrev_title>Wiki.J.Sci.</abbrev_title>
<issn media_type='electronic'>2002-4436 / 2470-6345 / 2639-5347</issn>
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<doi>10.15347/WJS</doi>
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<year>2024</year>
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<title>Poisson manifold</title>
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<surname>et al.</surname><affiliation>Wikipedia editors of Poisson manifold</affiliation><link>https://xtools.wmflabs.org/articleinfo/en.wikipedia.org/Poisson_manifold//2024-12-08</link>
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<year>2024</year>
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<resource>https://en.wikiversity.org/wiki/WikiJournal of Science/Poisson manifold</resource>
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This is an open access article distributed under the [http://creativecommons.org/licenses/by-sa/3.0/ Creative Commons Attribution ShareAlike License], which permits unrestricted use, distribution, and reproduction, provided the original author and source are credited.</license-p>
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In differential geometry, a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hamiltonian mechanics. A Poisson structure (or Poisson bracket) on a smooth manifold is a function on the vector space of smooth functions on , making it into a Lie algebra subject to a Leibniz rule (also known as a Poisson algebra). Poisson structures on manifolds were introduced by André Lichnerowicz in 1977 and are named after the French mathematician Siméon Denis Poisson, due to their early appearance in his works on analytical mechanics.
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