Theorems · Definition · nonassociative algebras

LieSubalgebra.comap

{R : Type u} →
  {L : Type v} →
    [inst : CommRing R] →
      [inst_1 : LieRing L] →
        [inst_2 : LieAlgebra R L] →
          {L₂ : Type w} →
            [inst_3 : LieRing L₂] → [inst_4 : LieAlgebra R L₂] → (L →ₗ⁅R⁆ L₂) → LieSubalgebra R L₂ → LieSubalgebra R L

The preimage of a Lie subalgebra under a Lie algebra morphism is a Lie subalgebra of the domain.

Defined in

Mathlib.Algebra.Lie.Subalgebra

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra