**Poisson Algebras**

Hamiltonian systems can be generalized in various ways. Instead of simply looking at the algebra of smooth functions over a symplectic manifold, Hamiltonian mechanics can be formulated on general commutative unital real Poisson algebras. A state is a continuous linear functional on the Poisson algebra (equipped with some suitable topology) such that for any element *A* of the algebra, *A*² maps to a nonnegative real number.

A further generalization is given by Nambu dynamics.

Read more about this topic: Hamiltonian Mechanics

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