Theorems · Definition · nonassociative algebras

UniversalEnvelopingAlgebra.lift

(R : Type u₁) →
  {L : Type u₂} →
    [inst : CommRing R] →
      [inst_1 : LieRing L] →
        [inst_2 : LieAlgebra R L] →
          {A : Type u₃} →
            [inst_3 : Ring A] → [inst_4 : Algebra R A] → (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)

The universal property of the universal enveloping algebra: Lie algebra morphisms into associative algebras lift to associative algebra morphisms from the universal enveloping algebra.

Defined in

Mathlib.Algebra.Lie.UniversalEnveloping

Cited by

7 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraRingAlgebra