OAI/GroupTheory/PolycyclicRecognition/Algebra/ClassTwoCommutatorPairing.lean

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9 declarations, 0 contain sorry, 0 declared as axioms

The actual central commutator pairing

For a group of class at most two, the commutator is a bilinear alternating map on its abelianization. The target here is the actual center, not a formal copy of the abelianization. This is the first central-layer map needed in the nilpotent homology argument.

  1. theorem OAI.PolycyclicRecognition.commutator_mul_left_of_central line 20
  2. theorem OAI.PolycyclicRecognition.commutator_mul_right_of_central line 27
  3. theorem OAI.PolycyclicRecognition.central_commutator_mul_left line 33
  4. theorem OAI.PolycyclicRecognition.central_commutator_mul_right line 40
  5. def OAI.PolycyclicRecognition.centerCommutatorLeft line 47
  6. def OAI.PolycyclicRecognition.centerCommutatorRight line 54
  7. def OAI.PolycyclicRecognition.centerCommutatorPairing line 64
  8. theorem OAI.PolycyclicRecognition.centerCommutatorPairing_of line 85
  9. theorem OAI.PolycyclicRecognition.centerCommutatorPairing_self line 92