How to show that the Lie derivative satisfies L[x,y]t = Lx(Ly(t)) - Ly(Lx(t))

[sadegh4137]

consider t is arbitrary tensor and [x,y] is Lie derivative
how can we show that

L_[x,y]t=L_x L_y t - L_y L_x t

 

[Fredrik]

Since this is a textbook-style question, the forum rules require you to post your own thoughts about this problem. Your post should include all the relevant definitions, and your work up to the point where you get stuck.