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A new construction of Moufang quadrangles of type E6, E7 and E8

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Abstract
In the classification of Moufang polygons by J. Tits and R. Weiss, the most intricate case is by far the case of the exceptional Moufang quadrangles of type E6, E7 and E8, and in fact, the construction that they present is ad-hoc and lacking a deeper explanation. We will show how tensor products of two composition algebras can be used to construct these Moufang quadrangles in characteristic different from 2. As a byproduct, we will obtain a method to construct any Moufang quadrangle in characteristic different from two from a module for a Jordan algebra.
Keywords
composition algebras, Moufang polygons, E6, E7, exceptional groups, linear algebraic groups, J-ternary algebras, Moufang quadrangles, FORMS, structurable algebras, Jordan algebras, octonion algebras, quadrangular algebras, ALGEBRAS, E8

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Chicago
Boelaert, Lien, and Tom De Medts. 2015. “A New Construction of Moufang Quadrangles of Type E6, E7 and E8.” Transactions of the American Mathematical Society 367 (5): 3447–3480.
APA
Boelaert, L., & De Medts, T. (2015). A new construction of Moufang quadrangles of type E6, E7 and E8. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 367(5), 3447–3480.
Vancouver
1.
Boelaert L, De Medts T. A new construction of Moufang quadrangles of type E6, E7 and E8. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 2015;367(5):3447–80.
MLA
Boelaert, Lien, and Tom De Medts. “A New Construction of Moufang Quadrangles of Type E6, E7 and E8.” TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 367.5 (2015): 3447–3480. Print.
@article{4157764,
  abstract     = {In the classification of Moufang polygons by J. Tits and R. Weiss, the most intricate case is by far the case of the exceptional Moufang quadrangles of type E6, E7 and E8, and in fact, the construction that they present is ad-hoc and lacking a deeper explanation. We will show how tensor products of two composition algebras can be used to construct these Moufang quadrangles in characteristic different from 2. As a byproduct, we will obtain a method to construct any Moufang quadrangle in characteristic different from two from a module for a Jordan algebra.},
  author       = {Boelaert, Lien and De Medts, Tom},
  issn         = {0002-9947},
  journal      = {TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY},
  keywords     = {composition algebras,Moufang polygons,E6,E7,exceptional groups,linear algebraic groups,J-ternary algebras,Moufang quadrangles,FORMS,structurable algebras,Jordan algebras,octonion algebras,quadrangular algebras,ALGEBRAS,E8},
  language     = {eng},
  number       = {5},
  pages        = {3447--3480},
  title        = {A new construction of Moufang quadrangles of type E6, E7 and E8},
  url          = {http://dx.doi.org/10.1090/S0002-9947-2014-06195-3},
  volume       = {367},
  year         = {2015},
}

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