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 #m/thm/lie

Proof

Since for any

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

#state/tidy | #lang/en | #SemBr

Footnotes

  1. where . ↩

  2. i.e. for some . ↩

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