a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which...

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...

by a Hamiltonian over a Poisson manifold. In 1973, Yoichiro Nambu suggested a generalization involving Nambu–Poisson manifolds with more than one Hamiltonian...

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...

derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra...

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...

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...

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...

Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation...

of a Poisson manifold. A multisymplectic manifold of degree k is a manifold equipped with a closed nondegenerate k-form. A polysymplectic manifold is a...