= Algebraic exponential of a locally nilpotent operator
{title2=$\exp(T)v=\sum_{j\geq0}T^jv/j!$}
Over a field of characteristic zero, a <locally nilpotent operator> has an algebraically defined exponential, because the sum is finite for each vector. Its inverse is $\exp(-T)$. The nilpotence bound may depend on the vector. In an <sl2 Lie algebra> <Verma module>, the raising operator is locally nilpotent but the lowering operator is not, so the latter's exponential does not define an endomorphism of the ordinary algebraic module.
// Target: lie-algebra.bigb
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