= Symmetric-part ambiguity in Maurer-Cartan coefficients
{title2=$f^\gamma{}_{[\alpha\beta]}=-\tfrac12c^\gamma{}_{\alpha\beta}$}
When $d\sigma^\gamma=\sum_{\alpha,\beta}f^\gamma{}_{\alpha\beta}\sigma^\alpha\wedge\sigma^\beta$ sums over ordered pairs, the <Maurer-Cartan equation> determines only $f^\gamma{}_{[\alpha\beta]}=-c^\gamma{}_{\alpha\beta}/2$. Symmetric additions vanish in the <exterior product>. The usual coefficients are the unique antisymmetric representatives; summing instead over $\alpha<\beta$ removes the factor one half.
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