I meet with this problem in my assignment.
Now G is an n-dimensional connected smooth Lie group and $ω^i$ i=1,...,n are the left invariant basis of smooth vector fields on G, i.e ,$w^i$ ,i=1,...,n are linearly independent at any point g∈G and for any i, $w^i$ is a left invariant vector field.
Assume σ: G → G is a smooth map and for i=1,....n , $w^i$ is σ-related to itself. I want to prove :
σ=$L_{σ(e)}$ .
I tried several methods but could not get any inspiration. I would apperciate if anyone could give a hint of the solution.