Theorems · Theorem · nonassociative algebras

LieSubalgebra.lie_mem_sup_of_mem_normalizer

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  {H : LieSubalgebra R L} {x y z : L},
  x ∈ H.normalizer → y ∈ R ∙ x ⊔ H.toSubmodule → z ∈ R ∙ x ⊔ H.toSubmodule → ⁅y, z⁆ ∈ R ∙ x ⊔ H.toSubmodule

Defined in

Mathlib.Algebra.Lie.Normalizer

Cited by

1 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra