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Exceptional Moufang quadrangles and structurable algebras

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Abstract
In 2000, J. Tits and R. Weiss classified all Moufang spherical buildings of rank 2, also known as Moufang polygons. The hardest case in the classification consists of the Moufang quadrangles. They fall into different families, each of which can be described by an appropriate algebraic structure. For the exceptional quadrangles, this description is intricate and involves many different maps that are defined ad hoc and lack a proper explanation. In this paper, we relate these algebraic structures to two other classes of algebraic structures that had already been studied before, namely to Freudenthal triple systems and to structurable algebras. We show that these structures give new insight into the understanding of the corresponding Moufang quadrangles.
Keywords
structurable algebras, Moufang quadrangles

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Citation

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MLA
Boelaert, Lien, and Tom De Medts. “Exceptional Moufang Quadrangles and Structurable Algebras.” PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY 107.3 (2013): 590–626. Print.
APA
Boelaert, L., & De Medts, T. (2013). Exceptional Moufang quadrangles and structurable algebras. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 107(3), 590–626.
Chicago author-date
Boelaert, Lien, and Tom De Medts. 2013. “Exceptional Moufang Quadrangles and Structurable Algebras.” Proceedings of the London Mathematical Society 107 (3): 590–626.
Chicago author-date (all authors)
Boelaert, Lien, and Tom De Medts. 2013. “Exceptional Moufang Quadrangles and Structurable Algebras.” Proceedings of the London Mathematical Society 107 (3): 590–626.
Vancouver
1.
Boelaert L, De Medts T. Exceptional Moufang quadrangles and structurable algebras. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. 2013;107(3):590–626.
IEEE
[1]
L. Boelaert and T. De Medts, “Exceptional Moufang quadrangles and structurable algebras,” PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, vol. 107, no. 3, pp. 590–626, 2013.
@article{4148061,
  abstract     = {{In 2000, J. Tits and R. Weiss classified all Moufang spherical buildings of rank 2, also known as Moufang polygons. The hardest case in the classification consists of the Moufang quadrangles. They fall into different families, each of which can be described by an appropriate algebraic structure. For the exceptional quadrangles, this description is intricate and involves many different maps that are defined ad hoc and lack a proper explanation.
In this paper, we relate these algebraic structures to two other classes of algebraic structures that had already been studied before, namely to Freudenthal triple systems and to structurable algebras. We show that these structures give new insight into the understanding of the corresponding Moufang quadrangles.}},
  author       = {{Boelaert, Lien and De Medts, Tom}},
  issn         = {{0024-6115}},
  journal      = {{PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY}},
  keywords     = {{structurable algebras,Moufang quadrangles}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{590--626}},
  title        = {{Exceptional Moufang quadrangles and structurable algebras}},
  url          = {{http://dx.doi.org/10.1112/plms/pds088}},
  volume       = {{107}},
  year         = {{2013}},
}

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