Parallelization of a Lie group by left translations
= Parallelization of a Lie group by left translations
{title2=$X_a(g)=(dL_g)_eT_a$}
A basis $T_a$ of the <Lie algebra> of a <Lie group> gives a global <frame of a vector bundle> of its <tangent bundle> by $X_a(g)=(dL_g)_eT_a$. Left translation is a <diffeomorphism>, so the <left-invariant vector fields> are independent everywhere. Every <Lie group> is therefore a <parallelizable manifold>.