Theorems · Definition · nonassociative algebras

LieIdeal.incl

{R : Type u} →
  {L : Type v} →
    [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → (I : LieIdeal R L) → ↥I →ₗ⁅R⁆ L

Regarding an ideal I as a subalgebra, the inclusion map into its ambient space is a morphism of Lie algebras.

Defined in

Mathlib.Algebra.Lie.Ideal

Cited by

17 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebra