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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, 
and [,] such that forms an associative K-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).
Examples
- The space of smooth functions over a symplectic manifold.
- If A is a noncommutative associative algebra, then the commutator [x,y]≡xy−yx turns it into a Poisson algebra.
See also
Poisson manifold, Poisson superalgebra, antibracket algebra
Last updated: 10-08-2005 13:01:53
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details