Theorems · Theorem · nonassociative algebras

LieDerivation.apply_lie_eq_sub

∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} [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]
  (D : LieDerivation R L M) (a b : L), D ⁅a, b⁆ = ⁅a, D b⁆ - ⁅b, D a⁆

Defined in

Mathlib.Algebra.Lie.Derivation.Basic

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses no axioms

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule