Theorems · Theorem · nonassociative algebras

lie_smul

∀ {R : Type u} {L : Type v} {M : Type w} [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] [LieModule R L M] (t : R) (x : L)
  (m : M), ⁅x, t • m⁆ = t • ⁅x, m⁆

Defined in

Mathlib.Algebra.Lie.Basic

Cited by

19 results in Mathlib

Foundations

Depth 9 from the axioms · uses no axioms

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule