= Invariant volume form on a Lie group
{title2=$\omega_g=(L_{g^{-1}})^*\omega_e$}
Choose a nonzero element of $\Lambda^nT_e^*G$ for an $n$-dimensional <Lie group> and transport it by inverse left translations. This gives a smooth nowhere-zero <left-invariant differential form> of top degree, hence an <orientation>. The identity $L_{(hg)^{-1}}L_h=L_{g^{-1}}$ proves invariance. The space of invariant top forms is one-dimensional, since evaluation at the identity identifies it with $\Lambda^nT_e^*G$.
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