OAI/NumberTheory/DukePrimeDegree/Dynamics/VelocityCommutant.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

The commutant of a block-supported actual velocity space

An element of a subgroup always conjugates its own velocity space to itself. Once that space has the block support found by recurrence and contains the within-block root directions, its commutant is the block scalar algebra (when no block is a singleton). This gives the full normalizer conclusion directly, without assuming that the subgroup is normalized by the diagonal group or invoking a Lie subgroup theorem.

  1. lemma OAI.DukePrimeDegree.slMatrixConjugation_mem_velocitySpace line 23
  2. theorem OAI.DukePrimeDegree.blockScalar_mem_iff_commute_velocitySpace line 33
  3. theorem OAI.DukePrimeDegree.subgroup_le_blockScalarNormalizer_of_velocity_support line 53