Theorems · Definition · nonassociative algebras

LieIdeal.map

{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' pushes forward Lie ideals of L to Lie ideals of L'. Note that unlike LieSubmodule.map, we must take the lieSpan of the image. Mathematically this is because although f makes L' into a Lie module over L, in general the L submodules of L' are not the same as the ideals of L'.

Defined in

Mathlib.Algebra.Lie.Ideal

Cited by

33 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieRingLieAlgebraLieAlgebra