Theorems · Theorem · nonassociative algebras

LieModule.exists_genWeightSpace_le_ker_of_isNoetherian

∀ {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] [IsNoetherian R M] (χ : L → R) (x : L),
  ∃ k,
    ↑(LieModule.genWeightSpace M χ) ≤
      LinearMap.ker (((LieModule.toEnd R L M) x - (algebraMap R (Module.End R M)) (χ x)) ^ k)

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

2 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotentIsNoetherian