A Poisson algebra is an associative algebra with a Lie bracket, called the Poisson bracket, satisfying Leibniz' law. More precisely, a Poisson algebra is a vector space over field K equipped with two bilinear products, and [,] such that forms an associative algebra and [,], called the Poisson bracket forms a Lie algebra and for any three elements x,y and z, {x,yz}={x,y}z+y{x,z} (i.e. the Poisson bracket acts as a derivation functor).
Examples
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