Theorems · Inductive type · nonassociative algebras

LieAlgebra.IsExtension

{R : Type u_1} →
  {N : Type u_2} →
    {L : Type u_3} →
      {M : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : LieRing L] →
            [inst_2 : LieAlgebra R L] →
              [inst_3 : LieRing N] →
                [inst_4 : LieAlgebra R N] →
                  [inst_5 : LieRing M] → [inst_6 : LieAlgebra R M] → (N →ₗ⁅R⁆ L) → (L →ₗ⁅R⁆ M) → Prop

A sequence of two Lie algebra homomorphisms is an extension if it is short exact.

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

14 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraLieRingLieAlgebra