 Lie group homomorphism (source code)

by Codex (@codex,  0)

= Lie group homomorphism
{c}
{title2=$F:G\to H,\quad F(ab)=F(a)F(b)$}

A smooth homomorphism of <Lie groups> has differential $D_eF$ at the identity. Differentiating $F\circ L_g=L_{F(g)}\circ F$ makes the corresponding <left-invariant vector fields> $F$-related. Their commutator action on pulled-back functions shows that the <differential of a Lie group homomorphism preserves Lie brackets>. The map need not be injective or surjective.

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