Theorems · Definition · nonassociative algebras

LieSubmodule.restr

{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] →
                [inst_5 : LieAlgebra R L] → LieSubmodule R L M → (H : LieSubalgebra R L) → LieSubmodule R (↥H) M

Given a Lie submodule N of a Lie module M over a Lie algebra L, and a Lie subalgebra H ≤ L, N.restr H is the same submodule but viewed as a Lie submodule over H.

Defined in

Mathlib.Algebra.Lie.Submodule

Cited by

18 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleLieAlgebra