Theorems · Theorem · nonassociative algebras
LieModule.finite_genWeightSpace_ne_bot
∀ (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] [IsDomain R] [Module.IsTorsionFree R M] [IsNoetherian R M],
{χ | LieModule.genWeightSpace M χ ≠ ⊥}.Finite- Defined in
- Mathlib.Algebra.Lie.Weights.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredstatement · cited by 6,101
- Bot.botstatement · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- Set.Finitestatement · cited by 1,814
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieRingModulestatement and proof · cited by 727
- Module.IsTorsionFreestatement and proof · cited by 600
- LieSubmodulestatement · cited by 489
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.eventually_genWeightSpace_smul_add_eq_botproof · cited by 4