OAI/GroupTheory/PolycyclicRecognition/Lattices/TriangulableLatticePolycyclic.lean
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Polycyclicity of lattices in the actual triangulable model
Finite generation comes from compactness and metric chains. The real triangular adjoint representation then identifies a polycyclic kernel and abelian height quotient. No lattice structure theorem is assumed for this specialization.
- theorem
OAI.PolycyclicRecognition.isPolycyclic_uniformLattice_of_realTriangulableline 22Source documentation
The uniform-lattice polycyclicity theorem for a real-triangulable, connected simply connected solvable Lie model.
theorem isPolycyclic_uniformLattice_of_realTriangulable (S : SimplyConnectedSolvableLieModel) (hS : IsRealTriangulable S) (Λ : Subgroup S.carrier) (hΛ : IsUniformLattice Λ) : IsPolycyclic Λ := by …Mentions: OAI.PolycyclicRecognition.SimplyConnectedSolvableLieModel, OAI.PolycyclicRecognition.IsRealTriangulable, OAI.PolycyclicRecognition.IsPolycyclic