Theorems · Theorem · nonassociative algebras

LieIdeal.le_killingCompl_top_of_isLieAbelian

∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L)
  [Module.Free R L] [Module.Finite R L] [IsDomain R] [IsPrincipalIdealRing R] [IsLieAbelian ↥I],
  I ≤ LieIdeal.killingCompl R L ⊤

Defined in: Mathlib.Algebra.Lie.TraceForm
Cited by: 1 results in Mathlib
Foundations: Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing LieAlgebra Module.Free Module.Finite IsDomain IsPrincipalIdealRing IsLieAbelian

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Top.topstatement and proof · cited by 9,680
IsDomainstatement and proof · cited by 2,196
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246
Module.Finitestatement and proof · cited by 1,032
Module.Freestatement and proof · cited by 597
LieIdealstatement and proof · cited by 282
IsPrincipalIdealRingstatement and proof · cited by 131
IsLieAbelianstatement and proof · cited by 55
killingFormproof · cited by 34

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.IsKilling.ideal_eq_bot_of_isLieAbelianproof · cited by 1