Theorems · Theorem · nonassociative algebras

LieAlgebra.ad_lie

∀ (R : Type u) {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (x y z : L),
  ((LieAlgebra.ad R L) x) ⁅y, z⁆ = ⁅((LieAlgebra.ad R L) x) y, z⁆ + ⁅y, ((LieAlgebra.ad R L) x) z⁆

Defined in

Mathlib.Algebra.Lie.OfAssociative

Cited by

0 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebra