A new construction of Moufang quadrangles of type E6, E7 and E8
Rings and Algebras
2013-05-23 v2
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 two from a module for a Jordan algebra.
Keywords
Cite
@article{arxiv.1301.6094,
title = {A new construction of Moufang quadrangles of type E6, E7 and E8},
author = {Lien Boelaert and Tom De Medts},
journal= {arXiv preprint arXiv:1301.6094},
year = {2013}
}
Comments
44 pages