Theorems · Theorem · nonassociative algebras

LieAlgebra.LieEquiv.ofCoboundary_toFun

∀ {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 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M]
  (c c' : ↥(LieModule.Cohomology.twoCocycle R L M)) (x : LieModule.Cohomology.oneCochain R L M)
  (h : ↑c' = ↑c + (LieModule.Cohomology.d₁₂ R L M) x) (y : LieAlgebra.ofTwoCocycle c),
  (LieAlgebra.LieEquiv.ofCoboundary c c' x h) y =
    (LieAlgebra.ofProd c')
      (((LieAlgebra.ofProd c).symm y).1, ((LieAlgebra.ofProd c).symm y).2 - x ((LieAlgebra.ofProd c).symm y).1)

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

0 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule