Theorems · Theorem · nonassociative algebras

IsSl2Triple.lie_h_pow_toEnd_e

∀ {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},
  IsSl2Triple h e f →
    ⁅h, m⁆ = μ • m →
      ∀ (n : ℕ), ⁅h, ((LieModule.toEnd R L M) e ^ n) m⁆ = (μ + 2 * ↑n) • ((LieModule.toEnd R L M) e ^ n) m

Defined in

Mathlib.Algebra.Lie.Sl2

Cited by

1 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule