Maurer-Cartan equation in a Lie-algebra basis
= Maurer-Cartan equation in a Lie-algebra basis
{c}
If $\rho=\sigma^\alpha T_\alpha$ and $[T_\alpha,T_\beta]=c^\gamma{}_{\alpha\beta}T_\gamma$, then
$$
d\sigma^\gamma=-\frac12c^\gamma{}_{\alpha\beta}
\sigma^\alpha\wedge\sigma^\beta.
$$