The geometry of conjugation in Euclidean isometry groups
Document Type
Journal Article
Role
Author
Journal Title
L’Enseignement Mathématique
Publication Date
9-30-2025
Abstract
We describe the geometry of conjugation within any split subgroup H of the full isometry group G of n-dimensional Euclidean space. We prove that, for any h∈H, the conjugacy class [h]H of h is described geometrically by the move-set of its linearization, while the set of elements conjugating h to a given h′∈[h]H is described by the fix-set of the linearization of h′. Examples include all affine Coxeter groups, certain crystallographic groups, and the group G itself.
Repository Citation
Elizabeth Milićević, Petra Schwer, Anne Thomas, The geometry of conjugation in Euclidean isometry groups. Enseign. Math. (2025). https://doi.org/10.4171/lem/1100
COinS