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    <full_title>WikiJournal of Science/Poisson manifold</full_title>
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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//2024-11-01</link>
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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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