Theorems · Theorem · nonassociative algebras

LieModule.mem_weightSpace

∀ {R : Type u_2} {L : Type u_3} {M : Type u_4} [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] [inst_6 : LieModule R L M] (χ : L → R)
  (m : M), m ∈ LieModule.weightSpace M χ ↔ ∀ (x : L), ⁅x, m⁆ = χ x • m

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

2 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule