OAI/GroupTheory/PolycyclicRecognition/Algebra/UnitaryEnergyProjection.lean

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10 declarations, 0 contain sorry, 0 declared as axioms

Scalar projections of normalized unitary cocycles

Positive generator energy gives a scalar function with a fixed nonzero normalization. Its harmonic defect is bounded by the vector-valued defect.

  1. def OAI.PolycyclicRecognition.unitaryCocycleEnergy line 19
  2. theorem OAI.PolycyclicRecognition.unitaryCocycleEnergy_nonneg line 23
  3. theorem OAI.PolycyclicRecognition.unitaryCocycleEnergy_generator_bound line 27
  4. theorem OAI.PolycyclicRecognition.IsUnitaryCocycle.norm_word_energy_le line 33
  5. theorem OAI.PolycyclicRecognition.IsUnitaryCocycle.norm_wordLength_energy_le line 51
  6. def OAI.PolycyclicRecognition.unitaryCocycleProjection line 63
  7. theorem OAI.PolycyclicRecognition.unitaryCocycleProjection_word_bound line 66
  8. theorem OAI.PolycyclicRecognition.unitaryCocycleProjection_defect line 83
  9. theorem OAI.PolycyclicRecognition.unitaryCocycleProjection_defect_bound line 93
  10. theorem OAI.PolycyclicRecognition.exists_normalized_unitaryCocycleProjection line 113