Theorems · Definition · nonassociative algebras

LieModuleEquiv.symm

{R : Type u} →
  {L : Type v} →
    {M : Type w} →
      {N : Type w₁} →
        [inst : CommRing R] →
          [inst_1 : LieRing L] →
            [inst_2 : AddCommGroup M] →
              [inst_3 : AddCommGroup N] →
                [inst_4 : Module R M] →
                  [inst_5 : Module R N] →
                    [inst_6 : LieRingModule L M] → [inst_7 : LieRingModule L N] → (M ≃ₗ⁅R,L⁆ N) → N ≃ₗ⁅R,L⁆ M

Lie module equivalences are symmetric.

Defined in

Mathlib.Algebra.Lie.Basic

Cited by

12 results in Mathlib

Foundations

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

Assumes

CommRingLieRingAddCommGroupAddCommGroupModuleModuleLieRingModuleLieRingModule