The galaxy of Coxeter groups
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909641762406400 |
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| author | Rego, Yuri Santos Schwer, Petra |
| author_facet | Rego, Yuri Santos Schwer, Petra |
| contents | In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to study the isomorphism problem for Coxeter groups. We prove some structural results about this space, provide a full characterization in small ranks and propose many questions. In addition we survey known tools, results and conjectures. Along the way we show profinite rigidity of triangle Coxeter groups -- a result which is possibly of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_17038 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The galaxy of Coxeter groups Rego, Yuri Santos Schwer, Petra Group Theory 20F55 In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to study the isomorphism problem for Coxeter groups. We prove some structural results about this space, provide a full characterization in small ranks and propose many questions. In addition we survey known tools, results and conjectures. Along the way we show profinite rigidity of triangle Coxeter groups -- a result which is possibly of independent interest. |
| title | The galaxy of Coxeter groups |
| topic | Group Theory 20F55 |
| url | https://arxiv.org/abs/2211.17038 |