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Veronesean representations of Moufang planes

(2015) MICHIGAN MATHEMATICAL JOURNAL. 64(4). p.819-847
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Abstract
In 1901 Severi [18] proved that the complex quadric Veronese variety is determined by three algebraic/differential geometric properties. In 1984 Mazzocca and Me lone [10] obtained a combinatorial analogue of this result for finite quadric Veronese varieties. We make further abstraction of these properties to characterize Veronesean representations of all the Moufang projective planes defined over a quadratic alternative division algebra over an arbitrary field. In the process, new Veroneseans over a nonperfect field of characteristic 2 (related to purely inseparable field extensions) are found, and their corresponding projective representations of the associated groups studied. We show that these representations are indecomposable, but reducible, and determine their (irreducible) quotient and kernel.
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Citation

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

MLA
Krauss, O., et al. “Veronesean Representations of Moufang Planes.” MICHIGAN MATHEMATICAL JOURNAL, vol. 64, no. 4, 2015, pp. 819–47.
APA
Krauss, O., Schillewaert, J., & Van Maldeghem, H. (2015). Veronesean representations of Moufang planes. MICHIGAN MATHEMATICAL JOURNAL, 64(4), 819–847.
Chicago author-date
Krauss, O, J Schillewaert, and Hendrik Van Maldeghem. 2015. “Veronesean Representations of Moufang Planes.” MICHIGAN MATHEMATICAL JOURNAL 64 (4): 819–47.
Chicago author-date (all authors)
Krauss, O, J Schillewaert, and Hendrik Van Maldeghem. 2015. “Veronesean Representations of Moufang Planes.” MICHIGAN MATHEMATICAL JOURNAL 64 (4): 819–847.
Vancouver
1.
Krauss O, Schillewaert J, Van Maldeghem H. Veronesean representations of Moufang planes. MICHIGAN MATHEMATICAL JOURNAL. 2015;64(4):819–47.
IEEE
[1]
O. Krauss, J. Schillewaert, and H. Van Maldeghem, “Veronesean representations of Moufang planes,” MICHIGAN MATHEMATICAL JOURNAL, vol. 64, no. 4, pp. 819–847, 2015.
@article{7047704,
  abstract     = {{In 1901 Severi [18] proved that the complex quadric Veronese variety is determined by three algebraic/differential geometric properties. In 1984 Mazzocca and Me lone [10] obtained a combinatorial analogue of this result for finite quadric Veronese varieties. We make further abstraction of these properties to characterize Veronesean representations of all the Moufang projective planes defined over a quadratic alternative division algebra over an arbitrary field. In the process, new Veroneseans over a nonperfect field of characteristic 2 (related to purely inseparable field extensions) are found, and their corresponding projective representations of the associated groups studied. We show that these representations are indecomposable, but reducible, and determine their (irreducible) quotient and kernel.}},
  author       = {{Krauss, O and Schillewaert, J and Van Maldeghem, Hendrik}},
  issn         = {{0026-2285}},
  journal      = {{MICHIGAN MATHEMATICAL JOURNAL}},
  keywords     = {{CAPS}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{819--847}},
  title        = {{Veronesean representations of Moufang planes}},
  volume       = {{64}},
  year         = {{2015}},
}

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