[TomOleDiem]

Summary

• `TranslationDual`: the characters of the translation group of a crystal (the crystal momenta).
• The symmetries of a crystal act on them by group automorphisms, via the inverse of their lattice automorphism.
• Pure translations act trivially.

The identification of the dual of a lattice with a torus, the reciprocal lattice and the Brillouin zone are left for later.

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For reviewers: Summary of your PR

Found differences:
@@ Physlib.CondensedMatter.Crystal.Symmetry.Dual @@
+ module added Physlib.CondensedMatter.Crystal.Symmetry.Dual (+146 -0)
  namespaces Physlib.CondensedMatter.Crystal
+ added abbrev TranslationDual
+ added def dualMap
+ added def pointAction
+ added def symmetryAction
+ added instance (C : Crystal G) :
+ added instance (C : Crystal G) : MulDistribMulAction (Symmetry C) (TranslationDual G)
+ added lemma Symmetry.smul_dual_apply
+ added lemma Symmetry.smul_dual_lattice
+ added lemma Symmetry.translation_smul_dual
+ added lemma mk_smul
+ added lemma translations_le_ker_symmetryAction
@@ Physlib @@
! module modified Physlib (+1 -0)
13 differences

The declarations are found by reading the diff as text, without regard for namespaces, so a declaration whose keyword and name are on different lines is missed, and two declarations of the same name in different namespaces are listed as one. A change to a proof, or to the body of a definition, does not appear. See scripts/alpha/github/pr_summary.lean.

Summary of commit dfde0eb, remade whenever a commit is pushed.

[jstoobysmith]

Symmetry namespace?

[jstoobysmith]

Would it be more physical to call TranslationDual, BrilloinZone

[jstoobysmith]

Namespace or name could be more descriptive