Lie algebra automorphism

Exponential of a derivation on a Lie algebra

Let be a Lie algebra over ¹, and be a nilpotent² derivation. Then the exponential

is a Lie algebra automorphism.³ lie

Proof

Since for any

it follows is a homomorphism, and an inverse is given by .

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Footnotes

1. where . ↩

2. i.e. for some . ↩

3. 1972. Introduction to Lie Algebras and Representation Theory, §2.3, pp. 8–9 ↩