Theorems · Theorem · nonassociative algebras

LieAlgebra.isExtension_of_surjective

∀ {R : Type u_1} {L : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : LieRing M] [inst_4 : LieAlgebra R M] (f : L →ₗ⁅R⁆ M),
  Function.Surjective ⇑f → LieAlgebra.IsExtension f.ker.incl f

A surjective Lie algebra homomorphism yields an extension.

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra