Theorems · Definition · nonassociative algebras

LieHom.quotKerEquivRange

{R : Type u_1} →
  {L : Type u_2} →
    {L' : Type u_3} →
      [inst : CommRing R] →
        [inst_1 : LieRing L] →
          [inst_2 : LieAlgebra R L] →
            [inst_3 : LieRing L'] → [inst_4 : LieAlgebra R L'] → (f : L →ₗ⁅R⁆ L') → (L ⧸ f.ker) ≃ₗ⁅R⁆ ↥f.range

The first isomorphism theorem for morphisms of Lie algebras.

Defined in

Mathlib.Algebra.Lie.Quotient

Cited by

3 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra