= Primitive exterior square
{title2=$\Lambda_0^2V$}
The primitive exterior square of a <symplectic vector space> is the <kernel> of its <symplectic contraction of an exterior square>. In <dimension> four, the invariant inverse-form bivector $\Omega$ has nonzero wedge square. Choose $\operatorname{vol}=\Omega\wedge\Omega/2$; the <symmetric bilinear form> $\xi\wedge\eta=B(\xi,\eta)\operatorname{vol}$ is <nondegenerate> on $\Lambda^2V$. The primitive subspace is $\Omega^\perp$, and therefore inherits a nondegenerate form of dimension five. The <symplectic Lie algebra> acts on it by infinitesimal <orthogonal transformations>.
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