Theorems · Theorem · nonassociative algebras
LieIdeal.root_apply_eq_zero_of_notMem_rootSet
∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : LieRing L] [inst_2 : LieAlgebra K L]
[inst_3 : FiniteDimensional K L] {H : LieSubalgebra K L} [inst_4 : H.IsCartanSubalgebra] [CharZero K]
[LieAlgebra.IsKilling K L] [LieModule.IsTriangularizable K (↥H) L] (I : LieIdeal K L) {h : ↥H},
↑h ∈ I → ∀ {β : ↥LieSubalgebra.root}, β ∉ I.rootSet → ↑β h = 0- Defined in
- Mathlib.Algebra.Lie.Weights.IsSimple
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- CharZerostatement and proof · cited by 932
- LieSubalgebrastatement and proof · cited by 418
- LieIdealstatement and proof · cited by 282
- LieModule.Weightstatement and proof · cited by 172
- LieSubmodule.toSubmoduleproof · cited by 150
Cited by2
Results whose statement or proof uses this declaration.
- LieIdeal.rootSet_apply_coroot_eq_zero_of_notMem_rootSetproof · cited by 2
- LieIdeal.restr_inf_cartan_eq_biSup_corootSubmoduleproof · cited by 1