Theorems · Theorem · nonassociative algebras

LieAlgebra.Extension.bracket

∀ {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] [inst_6 : LieRingModule L M]
  [inst_7 : LieModule R L M] (c : ↥(LieModule.Cohomology.twoCocycle R L M))
  (x y : (LieAlgebra.Extension.ofTwoCocycle c).L),
  ⁅x, y⁆ = (LieAlgebra.Extension.ofAlg c) ⁅(LieAlgebra.Extension.ofAlg c).symm x, (LieAlgebra.Extension.ofAlg c).symm y⁆

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraIsLieAbelianLieRingModuleLieModule