Theorems · Theorem · nonassociative algebras
LieIdeal.reflectionPerm_mem_rootSet_iff
∀ {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] [inst_5 : CharZero K]
[inst_6 : LieAlgebra.IsKilling K L] [inst_7 : LieModule.IsTriangularizable K (↥H) L] (I : LieIdeal K L)
(α β : ↥LieSubalgebra.root), ((LieAlgebra.IsKilling.rootSystem H).reflectionPerm β) α ∈ I.rootSet ↔ α ∈ I.rootSet- Defined in
- Mathlib.Algebra.Lie.Weights.IsSimple
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Setstatement · cited by 53,352
- RingHom.idstatement · cited by 18,349
- Finsetstatement · cited by 13,712
- Equivstatement · cited by 8,337
- 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
- RootPairingproof · cited by 710
- Module.Dualstatement and proof · cited by 583
Cited by1
Results whose statement or proof uses this declaration.
- LieIdeal.rootSpan_mem_invtRootSubmoduleproof · cited by 1