Theorems · Theorem · nonassociative algebras

LieModule.iSup_genWeightSpace_eq_top

∀ (K : Type u_1) (L : Type u_3) (M : Type u_4) [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M]
  [inst_3 : LieRing.IsNilpotent L] [inst_4 : Field K] [inst_5 : LieAlgebra K L] [inst_6 : Module K M]
  [inst_7 : LieModule K L M] [FiniteDimensional K M] [LieModule.IsTriangularizable K L M],
  ⨆ χ, LieModule.genWeightSpace M χ = ⊤

For a triangularizable Lie module in finite dimensions, the weight spaces span the entire space. See also LieModule.iSup_genWeightSpace_eq_top'.

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

4 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingAddCommGroupLieRingModuleLieRing.IsNilpotentFieldLieAlgebraModuleLieModuleFiniteDimensionalLieModule.IsTriangularizable