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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.17443 |
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| _version_ | 1866914728373125120 |
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| author | Neyt, Yannick Parkinson, James Van Maldeghem, Hendrik |
| author_facet | Neyt, Yannick Parkinson, James Van Maldeghem, Hendrik |
| contents | An automorphism of a building is called uniclass if the Weyl distance between any chamber and its image lies in a single (twisted) conjugacy class of the Coxeter group. In this paper we characterise uniclass automorphisms of spherical buildings in terms of their fixed structure. For this purpose we introduce the notion of a Weyl substructure in a spherical building. We also link uniclass automorphisms to the Freudenthal--Tits magic square. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17443 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniclass automorphisms of spherical buildings Neyt, Yannick Parkinson, James Van Maldeghem, Hendrik Group Theory An automorphism of a building is called uniclass if the Weyl distance between any chamber and its image lies in a single (twisted) conjugacy class of the Coxeter group. In this paper we characterise uniclass automorphisms of spherical buildings in terms of their fixed structure. For this purpose we introduce the notion of a Weyl substructure in a spherical building. We also link uniclass automorphisms to the Freudenthal--Tits magic square. |
| title | Uniclass automorphisms of spherical buildings |
| topic | Group Theory |
| url | https://arxiv.org/abs/2403.17443 |