Exponential of a nilpotent Lie algebra derivation ($\exp D={\sum }_{j=0}^{N-1}{D}^j/j!$)

Over a field of characteristic zero, a nilpotent operator $D$ which is a derivation of a Lie algebra exponentiates to a Lie algebra automorphism. The iterated rulefollows by induction using Pascal's identity. Regrouping the finite expansion of $[\exp (D)x,\exp (D)y]$ by total degree gives $\exp (D)[x,y]$. The inverse is $\exp (-D)$. This factorial construction must not be reduced naively to small positive characteristic.