Talk:Poisson algebra

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The only reference given declares the associative product in a Poison algebra to be commutative.--345Kai (talk) 21:27, 14 April 2016 (UTC)

Huh? Oh, I see. The Springer EOM article assumes this from the get-go. An explicit counterexample can be found in the construction of the tensor algebra of a Lie algebra, which is given in the article on universal enveloping algebras. The Lie-bracket product lifts up to become the Poisson bracket, while the associative product is just the tensor product used to build the tensor algebra: it is neither commutative nor is it anti-commutative; its merely associative. (talk) 17:52, 22 September 2016 (UTC)