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Automorphisms and opposition in twin buildings

Alice Devillers, James Parkinson and Hendrik Van Maldeghem (UGent)
(2013) JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. 94(2). p.189-201
Author
Organization
Abstract
We show that every automorphism of a thick twin building interchanging the halves of the building maps some residue to an opposite one. Furthermore, we show that no automorphism of a locally finite 2-spherical twin building of rank at least 3 maps every residue of one fixed type to an opposite (a key step in the proof is showing that every duality of a thick finite projective plane admits an absolute point). Our results also hold for all finite irreducible spherical buildings of rank at least 3, and imply that every involution of a thick irreducible finite spherical building of rank at least 3 has a fixed residue.
Keywords
(B_N)-PAIR, spherical buildings, KAC-MOODY GROUPS, projective planes, twin buildings, COLLINEATIONS

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Citation

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MLA
Devillers, Alice, et al. “Automorphisms and Opposition in Twin Buildings.” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol. 94, no. 2, 2013, pp. 189–201, doi:10.1017/S1446788712000481.
APA
Devillers, A., Parkinson, J., & Van Maldeghem, H. (2013). Automorphisms and opposition in twin buildings. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 94(2), 189–201. https://doi.org/10.1017/S1446788712000481
Chicago author-date
Devillers, Alice, James Parkinson, and Hendrik Van Maldeghem. 2013. “Automorphisms and Opposition in Twin Buildings.” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY 94 (2): 189–201. https://doi.org/10.1017/S1446788712000481.
Chicago author-date (all authors)
Devillers, Alice, James Parkinson, and Hendrik Van Maldeghem. 2013. “Automorphisms and Opposition in Twin Buildings.” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY 94 (2): 189–201. doi:10.1017/S1446788712000481.
Vancouver
1.
Devillers A, Parkinson J, Van Maldeghem H. Automorphisms and opposition in twin buildings. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. 2013;94(2):189–201.
IEEE
[1]
A. Devillers, J. Parkinson, and H. Van Maldeghem, “Automorphisms and opposition in twin buildings,” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol. 94, no. 2, pp. 189–201, 2013.
@article{6834567,
  abstract     = {{We show that every automorphism of a thick twin building interchanging the halves of the building maps some residue to an opposite one. Furthermore, we show that no automorphism of a locally finite 2-spherical twin building of rank at least 3 maps every residue of one fixed type to an opposite (a key step in the proof is showing that every duality of a thick finite projective plane admits an absolute point). Our results also hold for all finite irreducible spherical buildings of rank at least 3, and imply that every involution of a thick irreducible finite spherical building of rank at least 3 has a fixed residue.}},
  author       = {{Devillers, Alice and Parkinson, James and Van Maldeghem, Hendrik}},
  issn         = {{1446-7887}},
  journal      = {{JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY}},
  keywords     = {{(B_N)-PAIR,spherical buildings,KAC-MOODY GROUPS,projective planes,twin buildings,COLLINEATIONS}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{189--201}},
  title        = {{Automorphisms and opposition in twin buildings}},
  url          = {{http://doi.org/10.1017/S1446788712000481}},
  volume       = {{94}},
  year         = {{2013}},
}
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