Theorems · Theorem · nonassociative algebras

LieDerivation.apply_lie_eq_add

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  (D : LieDerivation R L L) (a b : L), D ⁅a, b⁆ = ⁅a, D b⁆ + ⁅D a, b⁆

For a Lie derivation from a Lie algebra to itself, the usual Leibniz rule holds.

Defined in

Mathlib.Algebra.Lie.Derivation.Basic

Cited by

1 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext

Assumes

CommRingLieRingLieAlgebra