Theorems · Definition · nonassociative algebras

LieModuleHom.restrictLie

{R : Type u} →
  {L : Type v} →
    [inst : CommRing R] →
      [inst_1 : LieRing L] →
        [inst_2 : LieAlgebra R L] →
          {M : Type w} →
            [inst_3 : AddCommGroup M] →
              [inst_4 : LieRingModule L M] →
                {N : Type w₁} →
                  [inst_5 : AddCommGroup N] →
                    [inst_6 : LieRingModule L N] →
                      [inst_7 : Module R N] →
                        [inst_8 : Module R M] → (M →ₗ⁅R,L⁆ N) → (L' : LieSubalgebra R L) → M →ₗ⁅R,↥L'⁆ N

An L-equivariant map of Lie modules M → N is L'-equivariant for any Lie subalgebra L' ⊆ L.

Defined in

Mathlib.Algebra.Lie.Subalgebra

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext

Assumes

CommRingLieRingLieAlgebraAddCommGroupLieRingModuleAddCommGroupLieRingModuleModuleModule