Theorems · Definition · nonassociative algebras

LieSubmodule.Quotient.lieSubmoduleInvariant

{R : Type u} →
  {L : Type v} →
    {M : Type w} →
      [inst : CommRing R] →
        [inst_1 : LieRing L] →
          [inst_2 : AddCommGroup M] →
            [inst_3 : Module R M] →
              [inst_4 : LieRingModule L M] →
                {N : LieSubmodule R L M} →
                  [inst_5 : LieAlgebra R L] → [LieModule R L M] → L →ₗ[R] ↥((↑N).compatibleMaps ↑N)

Given a Lie module M over a Lie algebra L, together with a Lie submodule N ⊆ M, there is a natural linear map from L to the endomorphisms of M leaving N invariant.

Defined in

Mathlib.Algebra.Lie.Quotient

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleLieAlgebraLieModule