I'm studying left-translation maps and left-invariant vector fields for Lie groups.
Vector addition is the group operation in this case.
Let v $\in$ $\Bbb R$n.
For $$L_v: \Bbb R^n \rightarrow \Bbb R^n$$
I found the left-translation map -
$$L_v= v+x$$
I'm trying to find the derivative $dL_v$ of said left-translation map.
If I take the derivative, I just get $1$. Something tells me it's a bit more complicated than that. Is there special way of taking the derivative of a left-translation map? What would $dL_v$ be in this case?