Theorems · Theorem · nonassociative algebras

LieAlgebra.Extension.oneCochainOfTwoSplitting_apply

∀ {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}
  (hs₁ : Function.LeftInverse ⇑E.proj ⇑s₁) (hs₂ : Function.LeftInverse ⇑E.proj ⇑s₂) (x : L),
  (E.oneCochainOfTwoSplitting hs₁ hs₂) x = E.toKer.symm ⟨s₁ x - s₂ x, ⋯⟩

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

1 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra