Theorems · Theorem · nonassociative algebras

LieModule.iSup_ucs_eq_genWeightSpace_zero

∀ (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], ⨆ k, LieSubmodule.ucs k ⊥ = LieModule.genWeightSpace M 0

See also LieModule.iInf_lowerCentralSeries_eq_posFittingComp.

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotentIsNoetherian