Theorems · Definition · nonassociative algebras

LieAlgebra.Extension.toKer

{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] → (E : LieAlgebra.Extension R M L) → M ≃ₗ⁅R⁆ ↥E.proj.ker

The Lie algebra isomorphism from the kernel of an extension to the kernel of the projection.

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

8 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra