- Thread starter
- #1

I let q be any point in G, and let [tex]x_{t}(q) = y [/tex]. Also, [tex] L_{x}(y) = xy [/tex]. So I have [tex] L_x \circ x_{t} (q) = xy [/tex] and i want to show that [tex] x_t \circ L_{x} (q) = x_{t}(xq) = xy [/tex].

i'm having trouble showing the last statement that [tex] x_{t}(xq) = xy [/tex]. Since X is a left invariant vector field, i know that [tex] dL_{x}X_{q} = X_{xq} [/tex] and [tex] \frac{\partial x_t(q)}{\partial t} = X_{q} [/tex] since x_t is the flow of X. i can't figure out how to use these to get to my desired result however.

would someone mind offering hints on how to proceed?