Theorems · Theorem · nonassociative algebras

LieModule.mem_genWeightSpace

∀ {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]
  [inst_7 : LieRing.IsNilpotent L] (χ : L → R) (m : M),
  m ∈ LieModule.genWeightSpace M χ ↔ ∀ (x : L), ∃ k, (((LieModule.toEnd R L M) x - χ x • 1) ^ k) m = 0

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

3 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent