Theorems · Theorem · nonassociative algebras

IsSl2Triple.exists_hasPrimitiveVectorWith

∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M] {h e f : L}
  [IsDomain R] [CharZero R] [Nontrivial M] [Module.IsTorsionFree R M] [Module.Finite R M]
  [LieModule.IsTriangularizable R L M] (t : IsSl2Triple h e f), ∃ μ m, m ≠ 0 ∧ t.HasPrimitiveVectorWith m μ

Defined in: Mathlib.Algebra.Lie.Sl2
Cited by: 0 results in Mathlib
Foundations: Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing LieAlgebra AddCommGroup Module LieRingModule LieModule IsDomain CharZero Nontrivial Module.IsTorsionFree Module.Finite LieModule.IsTriangularizable

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DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Set.Elemproof · cited by 7,166
Set.rangeproof · cited by 4,705
Finiteproof · cited by 3,029
Nontrivialstatement and proof · cited by 2,416
IsDomainstatement and proof · cited by 2,196
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246
Module.Finitestatement and proof · cited by 1,032

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