An algebraic structure for Moufang quadrangles
Author(s)
Bibliographic Information
An algebraic structure for Moufang quadrangles
（Memoirs of the American Mathematical Society, no. 818）
American Mathematical Society, 2005
Available at 16 libraries
Note
"Volume 173, number 818 (third of 5 numbers)."
Includes bibliographical references (p. 99)
Description and Table of Contents
Description
Very recently, the classification of Moufang polygons has been completed by Tits and Weiss. Moufang $n$-gons exist for $n \in \{3, 4, 6, 8 \}$ only. For $n \in \{3, 6, 8 \}$, 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.
Table of Contents
Introduction Definition Some identities From quadrangular systems to Moufang quadrangles From Moufang quadrangles to quadrangular systems Some remarks Examples The classification Appendix A. Abelian quadrangular systems Bibliography.
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