Maurer-Cartan equation

The Maurer-Cartan equation is

d ρ + ρ \land ρ = 0

for the left-invariant form

ρ = g^{- 1} d g

.

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- Maurer-Cartan equation in a Lie-algebra basis Maurer-Cartan equation

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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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 313 / 2 / b / Solution
Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 313 / 3 / b / Solution

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