OAI/GroupTheory/PolycyclicRecognition/Analysis/LinearSupportSymmetries.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Algebraic support symmetries

The finite symmetry conclusion does not require a preselected norm or topology on the finite-dimensional height quotient.

  1. theorem OAI.PolycyclicRecognition.finite_linear_support_isometries line 20

    Source documentation

    The support norm supplies the topology used to prove finiteness. The result concerns the original algebraic linear equivalences.

    theorem finite_linear_support_isometries (D : SupportDatum W I B) :
        Set.Finite {A : W ≃ₗ[ℝ] W | ∀ w, D.segmentSupport (A w) = D.segmentSupport w} := by
    …

    Mentions: OAI.PolycyclicRecognition.SupportDatum

  2. def OAI.PolycyclicRecognition.linearSupportSymmetryGroup line 39

    Source documentation

    The algebraic finite group of possible segment-support symmetries.

    def linearSupportSymmetryGroup (D : SupportDatum W I B) : Subgroup (W ≃ₗ[ℝ] W) where
    …

    Mentions: OAI.PolycyclicRecognition.SupportDatum

  3. instance OAI.PolycyclicRecognition.(instance at line 48) line 48