Theorems · Theorem · nonassociative algebras

LieModule.eq_iSup_inf_genWeightSpace

∀ (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] (N : LieSubmodule K L M),
  N = ⨆ χ, N ⊓ LieModule.genWeightSpace M ⇑χ

Defined in: Mathlib.Algebra.Lie.Weights.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LieRing AddCommGroup LieRingModule LieRing.IsNilpotent Field LieAlgebra Module LieModule FiniteDimensional LieModule.IsTriangularizable

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Cites33

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Fieldstatement and proof · cited by 7,404
Bot.botproof · cited by 4,720
LE.le.transproof · cited by 3,151
iSupstatement and proof · cited by 2,415
le_antisymmproof · cited by 2,068
FiniteDimensionalstatement and proof · cited by 1,854
le_rflproof · cited by 1,558
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.lieIdeal_eq_iSup_inf_genWeightSpaceproof · cited by 1