Very recently, the classification of Moufang polygons has been completed by
Tits and Weiss. Moufang n-gons exist for n G {3,4,6,8} only. For n G {3,6,8},
the proof is nicely divided into two parts: first, it is shown that a Moufang n-gon
can be parametrized by a certain interesting algebraic structure, and secondly, these
algebraic structures are classified. The classification of Moufang quadrangles (n=4)
is not organized in this way due to the absence of a suitable algebraic structure.
The goal of this article is to present such a uniform algebraic structure for Moufang
quadrangles, and to classify these structures without referring back to the original
Moufang quadrangles from which they arise, thereby also providing a new proof for
the classification of Moufang quadrangles, which does consist of the division into
these two parts. We hope that these algebraic structures will prove to be interesting
in their own right.
Received by the editor September 19, 2002.
2000 Mathematics Subject Classification. 51E12, 16W10, 20E42.
Key words and phrases. Moufang quadrangles, quadrangular systems.
The author is a Research Assistant of the Fund for Scientific Research - Flanders (Belgium)
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