Theorems · Theorem · nonassociative algebras

LieModule.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} [self : LieModule R L M] (t : R) (x : L)
  (m : M), ⁅x, t • m⁆ = t • ⁅x, m⁆

A Lie module bracket is compatible with scalar multiplication in its second argument.

Defined in

Mathlib.Algebra.Lie.Basic

Cited by

1 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

LieModule