Lie algebra automorphism

Inner Lie algebra automorphism

An inner automorphism of a Lie algebra 𝔤 is given by e−ad𝑥, where ad𝑥 is the adjoint representation for some 𝑥 ∈𝔤. lie As the Exponential of a derivation on a Lie algebra it is an automorphism.¹ The set of all inner automorphisms Inn⁡𝔤 forms a normal subgroup of Aut⁡𝔤.

Proof of normal subgroup

proof

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Footnotes

1. 1972. Introduction to Lie Algebras and Representation Theory, §2.3, pp. 8–9 ↩