Notes for AKT-140228/0:41:45

[math]\displaystyle{ (A^g)^h = A^{(gh)} }[/math] ?

[math]\displaystyle{ \begin{align} (A^g)^h &= h^{-1}(g^{-1}Ag + g^{-1}\mathrm{d}g)h + h^{-1}\mathrm{d}h \\ &= (gh)^{-1}A(gh) + (gh)^{-1}\mathrm{d}(gh) + h^{-1}\mathrm{d}h\\ &= A^{(gh)} + h^{-1}\mathrm{d}h \end{align} }[/math]