Theorems · Theorem · nonassociative algebras

LieAlgebra.IsKilling.isLieAbelian_iff_subsingleton

∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [LieAlgebra.IsKilling R L] [Module.Free R L] [Module.Finite R L] [IsDomain R] [IsPrincipalIdealRing R],
  IsLieAbelian L ↔ Subsingleton L

Defined in

Mathlib.Algebra.Lie.Killing

Cited by

1 results in Mathlib

Foundations

Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieAlgebra.IsKillingModule.FreeModule.FiniteIsDomainIsPrincipalIdealRing