Poisson algebra
= Poisson algebra
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{title2=$\{fg,h\}=f\{g,h\}+g\{f,h\}$}
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A <Poisson algebra> is a commutative associative algebra with a <Lie bracket> that is a derivation in each argument. Smooth functions on a <symplectic manifold> are its standard example. The linear span of moment-map components may form a finite-dimensional Lie subalgebra, while closing those components under multiplication normally produces a much larger <Poisson algebra>.