A new construction of Moufang quadrangles of type 
and 
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 | References | Similar Articles | Additional Information
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 
, 
and 
, 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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, and 
, J. Algebra 252 (2002), no. 2, 394-410. 
over an arbitrary field, Transform. Groups 17 (2012), no. 1, 209-231. Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 17A75, 17A40, 17C40, 20G15, 20G41, 17C27, 51E12
Retrieve articles in all journals with MSC (2010): 17A75, 17A40, 17C40, 20G15, 20G41, 17C27, 51E12
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.
