Theorems · Theorem · nonassociative algebras
LieEquiv.isEngelian_iff
∀ {R : Type u₁} {L : Type u₂} {L₂ : Type u₃} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
[inst_3 : LieRing L₂] [inst_4 : LieAlgebra R L₂] (e : L ≃ₗ⁅R⁆ L₂),
LieAlgebra.IsEngelian R L ↔ LieAlgebra.IsEngelian R L₂- Defined in
- Mathlib.Algebra.Lie.Engel
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieEquivstatement and proof · cited by 86
- LieEquiv.symmproof · cited by 34
- LieAlgebra.IsEngelianstatement · cited by 5
- LieEquiv.surjectiveproof · cited by 2
- Function.Surjective.isEngelianproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizerproof · cited by 1