Editing Poisson algebra (section)

In [[mathematics]], a '''Poisson algebra''' is an [[associative algebra]] together with a [[Lie algebra|Lie bracket]] that also satisfies [[product rule|Leibniz's law]]; that is, the bracket is also a [[derivation (abstract algebra)|derivation]]. Poisson algebras appear naturally in [[Hamiltonian mechanics]], and are also central in the study of  [[quantum group]]s. [[Manifold]]s with a Poisson algebra structure are known as [[Poisson manifold]]s, of which the [[symplectic manifold]]s and the [[Poisson–Lie group]]s are a special case.  The algebra is named in honour of [[Siméon Denis Poisson]].