Theorems · Definition · nonassociative algebras

LieSubalgebra.inclusion

{R : Type u} →
  {L : Type v} →
    [inst : CommRing R] →
      [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → {K K' : LieSubalgebra R L} → K ≤ K' → ↥K →ₗ⁅R⁆ ↥K'

Given two nested Lie subalgebras K ⊆ K', the inclusion K ↪ K' is a morphism of Lie algebras.

Defined in

Mathlib.Algebra.Lie.Subalgebra

Cited by

6 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra