I was wondering if anyone has any insight into what the composition of the lie derivative would look like.
For example say you take the lie derivative of some p-form $ \omega $ with $X$ and then $Y$. Using Cartan's formula it looks something like this
$$ \mathcal{L}_Y(\mathcal{L}_X\omega) = (i_Yd+di_Y)(i_Xd\omega+d(i_X\omega))=i_Yd(i_Xd\omega) +di_Yi_Xd\omega + di_Yd(i_X\omega)$$
I was wondering if there are some simplifications that can be made that could get it into a familiar form.