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

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- by Lien Boelaert and Tom De Medts PDF
- Trans. Amer. Math. Soc.
**367**(2015), 3447-3480 Request permission

## 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
- MR Author ID: 1035849
- Email: lboelaer@cage.UGent.be
**Tom De Medts**- Affiliation: Department of Mathematics, Ghent University, Krijgslaan 281, S22, B-9000 Gent, Belgium
- MR Author ID: 701084
- ORCID: 0000-0002-9504-5353
- Email: tdemedts@cage.UGent.be
- Received by editor(s): January 25, 2013
- Received by editor(s) in revised form: May 14, 2013
- Published electronically: November 20, 2014
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3314813