= Exterior multiplication
{title2=$e(\omega)\alpha=\omega\wedge\alpha$}
Exterior multiplication by a fixed <differential form> is the linear operator taking the <wedge product of differential forms> on the left. For a one-form $\omega$, it raises degree by one. Anticommutativity gives $e(\omega)e(\eta)+e(\eta)e(\omega)=0$ for one-forms. On the <exterior algebra> of an inner product space, pairing this operation with contraction produces <Clifford multiplication> $c(v)=e(v^\flat)-\iota_v$.
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