The geometry of conjugation in Euclidean isometry groups

2024/07/10 by Elizabeth Milićević, Petra Schwer, Milićević, Elizabeth +3 · 1 citation
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2407.08078

openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 the fix-set of its linearization. Examples include all affine Coxeter groups, certain crystallographic groups, and the group G itself.

Cited by

• Conjugator length of locally compact groups of Euclidean isometries

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