Theorems · Theorem · nonassociative algebras

LieDerivation.iterate_apply_lie

∀ {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) (n : ℕ) (a b : L),
  (⇑D)^[n] ⁅a, b⁆ = ∑ ij ∈ Finset.HasAntidiagonal.antidiagonal n, n.choose ij.1 • ⁅(⇑D)^[ij.1] a, (⇑D)^[ij.2] b⁆

The general Leibniz rule for Lie derivatives.

Defined in

Mathlib.Algebra.Lie.Derivation.Basic

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra