Theorems · Theorem · nonassociative algebras
IsSl2Triple.HasPrimitiveVectorWith.lie_e
∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [inst_4 : LieRingModule L M] {h e f : L} {t : IsSl2Triple h e f} {m : M} {μ : R},
t.HasPrimitiveVectorWith m μ → ⁅e, m⁆ = 0- Defined in
- Mathlib.Algebra.Lie.Sl2
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- Bracket.bracketstatement · cited by 642
- IsSl2Triplestatement and proof · cited by 38
- IsSl2Triple.HasPrimitiveVectorWithstatement and proof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_fproof · cited by 3