CartanIntrinsicBridge.lean`

1 declarations, 0 contain sorry, 0 declared as axioms

Bridge absorption using the actual finite Dynkin expansion

theorem OAI.PolycyclicRecognition.CartanWordModel.exists_sequence_intrinsic_bridge_lifts line 38

Source documentation

The published finite Dynkin identity supplies the bridge polynomial.

theorem exists_sequence_intrinsic_bridge_lifts
    (b₀ : Basis (Fin (finrank ℝ (cartanRootIdeal H))) ℝ (cartanRootIdeal H))
    (γ₀ : M.Bases) {cell : Set (F.N.carrier × F.D.carrier)} (hcell : IsCompact cell)
    (hφ : ∀ d, F.action d = M.adjointGroupAutomorphism T F.N.equiv F.ExpN F.isExpN
      hbijN dynkinN
      (cartanLog H F.D.equiv F.ExpD
        hbijD d))
    (hpath : ∀ g : G, ∃ γ : ℝ → G, γ 0 = 1 ∧ γ 1 = g ∧
      ∀ t ∈ Icc (0 : ℝ) 1, ∀ u ∈ Icc (0 : ℝ) 1,
        dist (γ t) (γ u) ≤ dist 1 g * |t - u|)
    {Kπ : ℝ} (hKπ : 0 ≤ Kπ)
    (hLip : ∀ x y, ‖(π x).toAdd - (π y).toAdd‖ ≤ Kπ * dist x y)
…

Mentions: OAI.PolycyclicRecognition.cartanRootIdeal, OAI.PolycyclicRecognition.cartanLog