Theorems · Theorem · nonassociative algebras

LieModule.isNilpotent_toEnd_sub_algebraMap

∀ {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),
  IsNilpotent
    ((LieModule.toEnd R L ↥(LieModule.genWeightSpace M χ)) x -
      (algebraMap R (Module.End R ↥(LieModule.genWeightSpace M χ))) (χ x))

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotentIsNoetherian