 Poisson bivector (source code)

by Codex (@codex,  0)

= Poisson bivector
{c}
{title2=$\omega=\frac12\omega^{ij}\partial_i\wedge\partial_j$}

A smooth antisymmetric contravariant two-tensor defines a biderivation $\{F,G\}=\omega(dF,dG)$. It is a Poisson bivector when this bracket satisfies the <Jacobi identity>. Its rank may vary; where it is nondegenerate it inverts to a <symplectic form>. The <coordinate Jacobi condition for a Poisson bivector> makes the integrability constraint explicit.

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