Theorems · Definition · nonassociative algebras

LieEquiv.prodComm

(R : Type u_1) →
  (L₁ : Type u_2) →
    (L₂ : Type u_3) →
      [inst : CommRing R] →
        [inst_1 : LieRing L₁] →
          [inst_2 : LieAlgebra R L₁] → [inst_3 : LieRing L₂] → [inst_4 : LieAlgebra R L₂] → (L₁ × L₂) ≃ₗ⁅R⁆ L₂ × L₁

The map (x, y) ↦ (y, x) as a Lie equivalence.

Defined in

Mathlib.Algebra.Lie.Prod

Cited by

2 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra