Theorems · Definition · nonassociative algebras

LieEquiv.ofEq

{R : Type u} →
  {L₁ : Type v} →
    [inst : CommRing R] →
      [inst_1 : LieRing L₁] →
        [inst_2 : LieAlgebra R L₁] → (L₁' L₁'' : LieSubalgebra R L₁) → ↑L₁' = ↑L₁'' → ↥L₁' ≃ₗ⁅R⁆ ↥L₁''

Lie subalgebras that are equal as sets are equivalent as Lie algebras.

Defined in

Mathlib.Algebra.Lie.Subalgebra

Cited by

3 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebra