Theorems · Definition · nonassociative algebras

LieAlgebra.Extension.oneCochainOfTwoSplitting

{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) →
                  {s₁ s₂ : L →ₗ[R] E.L} →
                    Function.LeftInverse ⇑E.proj ⇑s₁ →
                      Function.LeftInverse ⇑E.proj ⇑s₂ → LieModule.Cohomology.oneCochain R L M

The 1-cochain attached to a pair of splittings of an extension.

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

3 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra