= Closure of the inverse of a nondegenerate Poisson bivector
{title2=$d\Omega=0$}
A nondegenerate <Poisson bivector> inverts to a <closed differential form> of degree two. Differentiating $S=P^{-1}$ gives $\partial_dS=-S(\partial_dP)S$. Contracting the <coordinate Jacobi condition for a Poisson bivector> with three copies of $S$ yields $\partial_iS_{jk}+\partial_jS_{ki}+\partial_kS_{ij}=0$, which is precisely closure of the resulting <symplectic form>. An overall sign in the inverse convention does not change closure.
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