Theorems · Theorem · nonassociative algebras

LieAlgebra.InvariantForm.atomistic

∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : LieRing L] [inst_2 : LieAlgebra K L] [Module.Finite K L]
  (Φ : LinearMap.BilinForm K L),
  Φ.Nondegenerate →
    LinearMap.BilinForm.lieInvariant L Φ →
      Φ.IsRefl →
        (∀ (I : LieIdeal K L), IsAtom I → ¬IsLieAbelian ↥I) → ∀ (I : LieIdeal K L), sSup {J | IsAtom J ∧ J ≤ I} = I

Defined in

Mathlib.Algebra.Lie.InvariantForm

Cited by

1 results in Mathlib

Foundations

Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLieRingLieAlgebraModule.Finite