Theorems · Theorem · nonassociative algebras

IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f

∀ {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 →
    ∀ (n : ℕ), ⁅e, ((LieModule.toEnd R L M) f ^ (n + 1)) m⁆ = ((↑n + 1) * (μ - ↑n)) • ((LieModule.toEnd R L M) f ^ n) m

Defined in

Mathlib.Algebra.Lie.Sl2

Cited by

3 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule