OAI/GroupTheory/PolycyclicRecognition/Geometry/ActualRotationLieAlgebra.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

1. theorem OAI.PolycyclicRecognition.unitsHom_inverse_one line 17
2. theorem OAI.PolycyclicRecognition.tangent_shadow_triangular line 28
3. theorem OAI.PolycyclicRecognition.ComplexWeightFactorModel.smoothRotationalModification_bracket line 42
4. def OAI.PolycyclicRecognition.ComplexWeightFactorModel.smoothRotationalModificationLieEquiv line 81

   Source documentation

   The actual graph has the real-shadow bracket in its original tangent coordinates.

   def smoothRotationalModificationLieEquiv :
       GroupLieAlgebra (𝓘(ℝ,E)) (F.SmoothRotationalModification hExp) ≃ₗ⁅ℝ⁆ CartanRealShadow T H where
   …

   Mentions: OAI.PolycyclicRecognition.CartanRealShadow

5. theorem OAI.PolycyclicRecognition.ComplexWeightFactorModel.smoothRotationalModification_triangularAdjoint line 93

   Source documentation

   The simultaneous real triangular basis belongs to the actual graph Lie algebra.

   theorem smoothRotationalModification_triangularAdjoint :
       ∃ m : ℕ, Nonempty
         (TriangularAdjoint (GroupLieAlgebra (𝓘(ℝ,E)) (F.SmoothRotationalModification hExp)) m) := by
   …

   Mentions: OAI.PolycyclicRecognition.TriangularAdjoint