Theorems · Inductive type · nonassociative algebras
IsSl2Triple
{L : Type u_2} → [LieRing L] → L → L → L → PropAn sl₂ triple within a Lie ring L is a triple of elements h, e, f obeying relations
which ensure that the Lie subalgebra they generate is equivalent to sl₂.
- Defined in
- Mathlib.Algebra.Lie.Sl2
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- LieRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LieRingstatement · cited by 1,548
Cited by50
Results whose statement or proof uses this declaration.
- IsSl2Triple.HasPrimitiveVectorWithstatement · cited by 15
- IsSl2Triple.lie_e_fstatement and proof · cited by 8
- LieAlgebra.IsKilling.finrank_rootSpace_eq_oneproof · cited by 6
- LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZerostatement · cited by 5
- IsSl2Triple.h_eq_corootstatement and proof · cited by 4
- IsSl2Triple.h_ne_zerostatement and proof · cited by 4
- IsSl2Triple.lie_h_e_nsmulstatement and proof · cited by 4
- LieAlgebra.IsKilling.chainTopCoeff_zero_rightproof · cited by 4
- IsSl2Triple.e_ne_zerostatement and proof · cited by 4
- IsSl2Triple.f_ne_zerostatement and proof · cited by 3
- LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_leproof · cited by 3
- LieAlgebra.IsKilling.sl2SubalgebraOfRootproof · cited by 3