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Uniclass automorphisms of spherical buildings

Yannick Neyt (UGent) , James parkinson and Hendrik Van Maldeghem (UGent)
(2025) GEOMETRIAE DEDICATA. 219.
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Abstract
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.
Keywords
Spherical building, Uniclass automorphism, Domestic automorphism, CONJUGACY CLASSES, INVOLUTIONS, OPPOSITION

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Please use this url to cite or link to this publication:

MLA
Neyt, Yannick, et al. “Uniclass Automorphisms of Spherical Buildings.” GEOMETRIAE DEDICATA, vol. 219, 2025, doi:10.1007/s10711-025-00988-6.
APA
Neyt, Y., parkinson, J., & Van Maldeghem, H. (2025). Uniclass automorphisms of spherical buildings. GEOMETRIAE DEDICATA, 219. https://doi.org/10.1007/s10711-025-00988-6
Chicago author-date
Neyt, Yannick, James parkinson, and Hendrik Van Maldeghem. 2025. “Uniclass Automorphisms of Spherical Buildings.” GEOMETRIAE DEDICATA 219. https://doi.org/10.1007/s10711-025-00988-6.
Chicago author-date (all authors)
Neyt, Yannick, James parkinson, and Hendrik Van Maldeghem. 2025. “Uniclass Automorphisms of Spherical Buildings.” GEOMETRIAE DEDICATA 219. doi:10.1007/s10711-025-00988-6.
Vancouver
1.
Neyt Y, parkinson J, Van Maldeghem H. Uniclass automorphisms of spherical buildings. GEOMETRIAE DEDICATA. 2025;219.
IEEE
[1]
Y. Neyt, J. parkinson, and H. Van Maldeghem, “Uniclass automorphisms of spherical buildings,” GEOMETRIAE DEDICATA, vol. 219, 2025.
@article{01JPMRZ6411JTVNSWEB3HGEJ11,
  abstract     = {{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.}},
  articleno    = {{34}},
  author       = {{Neyt, Yannick and parkinson, James and Van Maldeghem, Hendrik}},
  issn         = {{0046-5755}},
  journal      = {{GEOMETRIAE DEDICATA}},
  keywords     = {{Spherical building,Uniclass automorphism,Domestic automorphism,CONJUGACY CLASSES,INVOLUTIONS,OPPOSITION}},
  language     = {{eng}},
  pages        = {{54}},
  title        = {{Uniclass automorphisms of spherical buildings}},
  url          = {{http://doi.org/10.1007/s10711-025-00988-6}},
  volume       = {{219}},
  year         = {{2025}},
}
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