Theorems · Theorem · nonassociative algebras

LieModule.exists_genWeightSpace_smul_add_eq_bot

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (M : Type u_3)
  [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] (χ₁ χ₂ : L → R) [IsAddTorsionFree R] [IsDomain R] [Module.IsTorsionFree R M]
  [IsNoetherian R M], χ₁ ≠ 0 → ∃ k > 0, LieModule.genWeightSpace M (k • χ₁ + χ₂) = ⊥

Defined in

Mathlib.Algebra.Lie.Weights.Chain

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotentIsAddTorsionFreeIsDomainModule.IsTorsionFreeIsNoetherian