OAI/GroupTheory/PolycyclicRecognition/Geometry/CartanContractedRoots.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

The Cartan subgroup and its contracted root directions generate the group

Each nonzero generalized root contracts in a suitable Cartan direction. The nilpotent part of the adjoint operator is retained. The already constructed finite root words and Cartan factorization then prove generation.

  1. theorem OAI.PolycyclicRecognition.root_exp_mem_contracted_cartan line 31
  2. theorem OAI.PolycyclicRecognition.CartanWordModel.cartan_and_contracted_generate line 82