Theorems · Theorem · nonassociative algebras

killingForm_eq_zero_of_mem_zeroRoot_mem_posFitting

∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  (H : LieSubalgebra R L) [inst_3 : LieRing.IsNilpotent ↥H] {x₀ x₁ : L},
  x₀ ∈ LieAlgebra.zeroRootSubalgebra R L H → x₁ ∈ LieModule.posFittingComp R (↥H) L → ((killingForm R L) x₀) x₁ = 0

Defined in

Mathlib.Algebra.Lie.TraceForm

Cited by

1 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRing.IsNilpotent