nLab Hadamard's formula

Sometimes called Hadamard lemma, however, in $n$Lab, Hadamard lemma is another result of Jacques Hadamard, in analysis.

Geometrical motivation

Hadamard’s formula relates the Ad action of a Lie group on its tangent Lie algebra, with the ad action of the Lie algebra on itself.

Statement

$$e^X Y e^{-X} = e^{ad X} (Y)$$

References

• wikipedia Baker-Campbell-Hausdorff formula, section Hadarmard lemma.