Lie algebras MOC

Lie algebra automorphism

Let 𝔤 be a Lie algebra. An automorphism 𝜑 ∈Aut⁡𝔤 is an isomorphism 𝜑 :𝔤 →𝔤. #m/def/lie In particular,

1. If 𝔤 ≤𝔤𝔩(𝑉), then GL⁡(𝑉) ≤Aut⁡𝔤.
2. The Exponential of a derivation on a Lie algebra is an automorphism.
3. Applying the above to the adjoint representation yields Inner automorphisms Inn⁡𝔤 ⊴Aut⁡𝔤.

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