Theorems · Theorem · nonassociative algebras
IsSl2Triple.h_eq_coroot
∀ {K : Type u_2} {L : Type u_3} [inst : LieRing L] [inst_1 : Field K] [inst_2 : LieAlgebra K L]
[inst_3 : FiniteDimensional K L] {H : LieSubalgebra K L} [inst_4 : H.IsCartanSubalgebra]
[inst_5 : LieAlgebra.IsKilling K L] [LieModule.IsTriangularizable K (↥H) L] [CharZero K]
{α : LieModule.Weight K (↥H) L},
α.IsNonZero →
∀ {h e f : L},
IsSl2Triple h e f →
e ∈ LieAlgebra.rootSpace H ⇑α → f ∈ LieAlgebra.rootSpace H (-⇑α) → h = ↑(LieAlgebra.IsKilling.coroot α)- Defined in
- Mathlib.Algebra.Lie.Weights.Killing
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
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
- Fieldstatement and proof · cited by 7,404
- mul_oneproof · cited by 3,885
- FiniteDimensionalstatement and proof · cited by 1,854
- mul_assocproof · cited by 1,667
- LieRingstatement and proof · cited by 1,548
- LinearEquiv.symmproof · cited by 1,461
- one_smulproof · cited by 1,374
- LieAlgebrastatement and proof · cited by 1,246
- CharZerostatement and proof · cited by 932
- zero_smulproof · cited by 716
- Bracket.bracketproof · cited by 642
Cited by4
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.finrank_rootSpace_eq_oneproof · cited by 6
- LieAlgebra.IsKilling.chainTopCoeff_zero_rightproof · cited by 4
- LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_supproof · cited by 3
- LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_leproof · cited by 3