= Exponential of a nilpotent Lie algebra derivation
{title2=$\exp D=\sum_{j=0}^{N-1}D^j/j!$}
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 rule
$$
D^k[x,y]=\sum_{j=0}^k\binom{k}{j}[D^jx,D^{k-j}y]
$$
follows 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.
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