Theorems · Definition · nonassociative algebras

LinearEquiv.lieConj

{R : Type u} →
  {M₁ : Type v} →
    {M₂ : Type w} →
      [inst : CommRing R] →
        [inst_1 : AddCommGroup M₁] →
          [inst_2 : Module R M₁] →
            [inst_3 : AddCommGroup M₂] → [inst_4 : Module R M₂] → (M₁ ≃ₗ[R] M₂) → Module.End R M₁ ≃ₗ⁅R⁆ Module.End R M₂

A linear equivalence of two modules induces a Lie algebra equivalence of their endomorphisms.

Defined in

Mathlib.Algebra.Lie.OfAssociative

Cited by

4 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule