Theorems · Theorem · nonassociative algebras

LieAlgebra.InvariantForm.orthogonal_disjoint

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  (Φ : LinearMap.BilinForm R L),
  Φ.Nondegenerate →
    ∀ (hΦ_inv : LinearMap.BilinForm.lieInvariant L Φ),
      (∀ (I : LieIdeal R L), IsAtom I → ¬IsLieAbelian ↥I) →
        ∀ (I : LieIdeal R L), IsAtom I → Disjoint I (LieAlgebra.InvariantForm.orthogonal Φ hΦ_inv I)

Defined in

Mathlib.Algebra.Lie.InvariantForm

Cited by

3 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra