OAI/GroupTheory/PolycyclicRecognition/Analysis/ConnectedQuasiUnipotentAction.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Connected solvable actions with unipotent powers

Finite generation makes a torsion eigencharacter finite. Its kernel is dense in the connected polynomial topology, so the whole common eigenspace is fixed. Quotient-dimension induction then bounds all mixed operator words.

  1. theorem OAI.PolycyclicRecognition.PolynomialMatrixGroup.isClosed_vector_fixer line 21
  2. theorem OAI.PolycyclicRecognition.PolynomialMatrixGroup.connected_commonEigenspace_fixed line 36
  3. theorem OAI.PolycyclicRecognition.PolynomialMatrixGroup.connected_solvable_quasiUnipotent_words line 64