Theorems · Theorem · nonassociative algebras
IsSl2Triple.lie_e_f
∀ {L : Type u_2} [inst : LieRing L] {h e f : L}, IsSl2Triple h e f → ⁅e, f⁆ = h- Defined in
- Mathlib.Algebra.Lie.Sl2
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- LieRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LieRingstatement and proof · cited by 1,548
- Bracket.bracketstatement · cited by 642
- IsSl2Triplestatement and proof · cited by 38
Cited by8
Results whose statement or proof uses this declaration.
- IsSl2Triple.h_eq_corootproof · cited by 4
- IsSl2Triple.e_ne_zeroproof · cited by 4
- IsSl2Triple.f_ne_zeroproof · cited by 3
- LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_supproof · cited by 3
- IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_fproof · cited by 3
- IsSl2Triple.symmproof · cited by 2
- LieAlgebra.Basis.coroot_eq_h'proof · cited by 1
- IsSl2Triple.mem_toLieSubalgebra_iffproof · cited by 0