OAI/GroupTheory/PolycyclicRecognition/Algebra/InvariantSubspaceDeterminant.lean

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Determinants of scalar commutators on an invariant subspace

Restricting an action to a genuinely invariant subspace gives an action by linear equivalences. Its commutators have determinant one, so a scalar commutator has scalar a root of unity of degree the subspace dimension.

  1. def OAI.PolycyclicRecognition.invariantSubspaceAction line 19
  2. theorem OAI.PolycyclicRecognition.invariantSubspaceAction_scalar line 47
  3. theorem OAI.PolycyclicRecognition.scalar_commutator_root_of_unity line 54