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Let $V$ be a real inner product space and $C[V]$ its ${\rm C}^*$ Cliffordalgebra. We prove that if $Z$ is a subspace of $V$ then $C[Z^{\perp}]$coincides with the supercommutant of $C[Z]$ in $C[V]$.

'Twisted duality' in the ${\rm C^*}$ Clifford algebra