Theorems · Definition · nonassociative algebras

LieIdeal.comap

{R : Type u} →
  {L : Type v} →
    {L' : Type w₂} →
      [inst : CommRing R] →
        [inst_1 : LieRing L] →
          [inst_2 : LieRing L'] →
            [inst_3 : LieAlgebra R L'] → [inst_4 : LieAlgebra R L] → (L →ₗ⁅R⁆ L') → LieIdeal R L' → LieIdeal R L

A morphism of Lie algebras f : L → L' pulls back Lie ideals of L' to Lie ideals of L. Note that f makes L' into a Lie module over L (turning f into a morphism of Lie modules) and so this is a special case of LieSubmodule.comap but we do not exploit this fact.

Defined in

Mathlib.Algebra.Lie.Ideal

Cited by

21 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext

Assumes

CommRingLieRingLieRingLieAlgebraLieAlgebra