Theorems · Theorem · nonassociative algebras

IsSl2Triple.HasPrimitiveVectorWith.exists_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] [LieModule R L M] {h e f : L} {m : M}
  {μ : R} {t : IsSl2Triple h e f},
  t.HasPrimitiveVectorWith m μ → ∀ [IsNoetherian R M] [Module.IsTorsionFree R M] [IsDomain R] [CharZero R], ∃ n, μ = ↑n

The eigenvalue of a primitive vector must be a natural number if the representation is finite-dimensional.

Defined in

Mathlib.Algebra.Lie.Sl2

Cited by

2 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleIsNoetherianModule.IsTorsionFreeIsDomainCharZero