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

Boelaert, Lien; De Medts, Tom

doi:10.1090/S0002-9947-2014-06195-3

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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