ad_isIdealMorphism — Mathlib

English

The range of the adjoint action is an ideal morphism: ad is an ideal morphism.

Русский

Образ adj является идеалом-омной морфизм: adj — морфизм идеала.

LaTeX

$$ad-is-ideal-morphism$$

Lean4

/-- The range of the adjoint action homomorphism from a Lie algebra `L` to the Lie algebra of its
derivations is an ideal of the latter. -/
theorem ad_isIdealMorphism : (ad R L).IsIdealMorphism :=
  by
  simp_rw [LieHom.isIdealMorphism_iff, lie_der_ad_eq_ad_der]
  tauto

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