Theorems · Theorem · nonassociative algebras

LieAlgebra.Extension.twoCocycleOf_coe_coe

∀ {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] [inst_5 : IsLieAbelian M] (E : LieAlgebra.Extension R M L)
  {s : L →ₗ[R] E.L} (hs : Function.LeftInverse ⇑E.proj ⇑s),
  ↑↑(E.twoCocycleOf hs) = (LieAlgebra.Extension.twoCocycleAux✝ E hs).compr₂ ↑E.toKer.symm.toLinearEquiv

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraIsLieAbelian