• a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which...
    87 KB (12,668 words) - 06:56, 6 January 2025
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    more general sense, the Poisson bracket is used to define a Poisson algebra, of which the algebra of functions on a Poisson manifold is a special case. There...
    23 KB (4,025 words) - 03:53, 19 December 2024
  • by a Hamiltonian over a Poisson manifold. In 1973, Yoichiro Nambu suggested a generalization involving Nambu–Poisson manifolds with more than one Hamiltonian...
    6 KB (735 words) - 04:26, 12 February 2024
  • mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure...
    7 KB (1,124 words) - 10:10, 25 December 2024
  • of functions. If the odd Poisson bi-vector π i j {\displaystyle \pi ^{ij}} is invertible, one has an odd symplectic manifold. In that case, there exists...
    16 KB (3,114 words) - 07:36, 25 May 2024
  • derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra...
    6 KB (820 words) - 11:59, 4 October 2024
  • on an arbitrary Poisson manifold. The Lie bracket of two Hamiltonian vector fields corresponding to functions f and g on the manifold is itself a Hamiltonian...
    8 KB (1,155 words) - 18:01, 10 December 2024
  • be a deformation of the algebra of functions on a symplectic manifold or Poisson manifold. However, as a natural quantization scheme (a functor), Weyl's...
    11 KB (1,635 words) - 18:01, 3 January 2025
  • superalgebra. Every symplectic supermanifold is a Poisson supermanifold but not vice versa. Poisson manifold Poisson algebra Noncommutative geometry v t e...
    761 bytes (86 words) - 12:47, 8 May 2022
  • integrable. Symplectic manifolds are special cases of a Poisson manifold. A multisymplectic manifold of degree k is a manifold equipped with a closed...
    23 KB (3,665 words) - 17:58, 24 January 2025