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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A new construction of Moufang quadrangles of type $ E_6, E_7$ and $ E_8$


Authors: Lien Boelaert and Tom De Medts
Journal: Trans. Amer. Math. Soc. 367 (2015), 3447-3480
MSC (2010): Primary 17A75, 17A40, 17C40, 20G15, 20G41; Secondary 17C27, 51E12
DOI: https://doi.org/10.1090/S0002-9947-2014-06195-3
Published electronically: November 20, 2014
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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 $ E_6$, $ E_7$ and $ E_8$, 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 2 from a module for a Jordan algebra.


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Additional Information

Lien Boelaert
Affiliation: Department of Mathematics, Ghent University, Krijgslaan 281, S22, B-9000 Gent, Belgium
Email: lboelaer@cage.UGent.be

Tom De Medts
Affiliation: Department of Mathematics, Ghent University, Krijgslaan 281, S22, B-9000 Gent, Belgium
Email: tdemedts@cage.UGent.be

DOI: https://doi.org/10.1090/S0002-9947-2014-06195-3
Keywords: Moufang polygons, Moufang quadrangles, composition algebras, octonion algebras, quadrangular algebras, Jordan algebras, structurable algebras, $J$-ternary algebras, linear algebraic groups, exceptional groups, $E_6$, $E_7$, $E_8$
Received by editor(s): January 25, 2013
Received by editor(s) in revised form: May 14, 2013
Published electronically: November 20, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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