Theorems · Definition · nonassociative algebras

LieEquiv.ofSubalgebras

{R : Type u} →
  {L₁ : Type v} →
    {L₂ : Type w} →
      [inst : CommRing R] →
        [inst_1 : LieRing L₁] →
          [inst_2 : LieRing L₂] →
            [inst_3 : LieAlgebra R L₁] →
              [inst_4 : LieAlgebra R L₂] →
                (L₁' : LieSubalgebra R L₁) →
                  (L₂' : LieSubalgebra R L₂) →
                    (e : L₁ ≃ₗ⁅R⁆ L₂) → LieSubalgebra.map e.toLieHom L₁' = L₂' → ↥L₁' ≃ₗ⁅R⁆ ↥L₂'

An equivalence of Lie algebras restricts to an equivalence from any Lie subalgebra onto its image.

Defined in

Mathlib.Algebra.Lie.Subalgebra

Cited by

3 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieRingLieAlgebraLieAlgebra