Theorems · Theorem · nonassociative algebras

IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_ne_zero_of_eq_nat

∀ {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}
  {m : M} {μ : R} {t : IsSl2Triple h e f},
  t.HasPrimitiveVectorWith m μ →
    ∀ [CharZero R] [IsDomain R] [Module.IsTorsionFree R M] {n : ℕ},
      μ = ↑n → ∀ {i : ℕ}, i ≤ n → ((LieModule.toEnd R L M) f ^ i) m ≠ 0

Defined in

Mathlib.Algebra.Lie.Sl2

Cited by

2 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleCharZeroIsDomainModule.IsTorsionFree