= Complex Clifford spinor dimension
{title2=$\dim_{\mathbb C}\mathrm{Dirac}_{2k}=2^k$}
After complexifying a nondegenerate metric in $D=2k$ dimensions, pair <gamma matrices> into $k$ fermionic creation and annihilation operators. Their binary occupation states span $2^k$ dimensions, and the <gamma matrices> generate all endomorphisms of this space. The Dirac module is therefore irreducible as a Clifford module. The even algebra preserves the chirality grading, splitting its Lorentz-spinor representation into two irreducible Weyl modules of dimension $2^{k-1}$. In $D=2k+1$, adjoining the old <chirality matrix> as the extra gamma gives an irreducible $2^k$-dimensional <Spin group> representation with no Weyl splitting. The two possible signs of that extra gamma distinguish Clifford modules but give equivalent <Spin group> modules.
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