The geometry of conjugation in Euclidean isometry groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909709569622016 |
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| author | Milićević, Elizabeth Schwer, Petra Thomas, Anne |
| author_facet | Milićević, Elizabeth Schwer, Petra Thomas, Anne |
| contents | 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 $h \in H$, 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 $h'\in [h]_H$ is described by the the fix-set of its linearization. Examples include all affine Coxeter groups, certain crystallographic groups, and the group $G$ itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The geometry of conjugation in Euclidean isometry groups Milićević, Elizabeth Schwer, Petra Thomas, Anne Group Theory Geometric Topology 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 $h \in H$, 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 $h'\in [h]_H$ is described by the the fix-set of its linearization. Examples include all affine Coxeter groups, certain crystallographic groups, and the group $G$ itself. |
| title | The geometry of conjugation in Euclidean isometry groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2407.08078 |