Maurer-Cartan equation in a Lie-algebra basis

If

ρ = σ^{α} T_{α}

and

[T_{α}, T_{β}] = c^{γ}_{α β} T_{γ}

, then

d σ^{γ} = - \frac{1}{2} c^{γ}_{α β} σ^{α} \land σ^{β} .

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