Poisson algebra

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

Related Topics:
Associative algebra - Lie bracket - Leibniz' law - Vector space - Field - Bilinear - Poisson bracket - Lie algebra - Derivation

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