OAI/GroupTheory/PolycyclicRecognition/Finiteness/FiniteGroupProjectiveNorm.lean

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Norms on projective integral representations of finite groups

Every invariant vector in a free representation is a norm. Splitting the normalized free cover extends this to projective representations. Consequently, a scalar endomorphism of the trivial representation factors through a projective representation exactly when the group order divides that scalar.

  1. theorem OAI.PolycyclicRecognition.freeRepresentation_action_coeff line 20
  2. theorem OAI.PolycyclicRecognition.freeRepresentation_invariant_is_norm line 35
  3. theorem OAI.PolycyclicRecognition.projectiveRepresentation_invariant_is_norm line 56
  4. theorem OAI.PolycyclicRecognition.projective_trivial_factor_divisible line 72
  5. theorem OAI.PolycyclicRecognition.stableTrivialScalar_eq_zero_iff line 85