Exceptional Moufang quadrangles and structurable algebras

TL;DR

This paper links exceptional Moufang quadrangles to well-studied algebraic structures, namely Freudenthal triple systems and structurable algebras, providing new insights into their complex algebraic descriptions.

Contribution

It establishes a connection between exceptional Moufang quadrangles and known algebraic structures, simplifying their intricate algebraic descriptions.

Findings

Relates exceptional Moufang quadrangles to Freudenthal triple systems.

Connects Moufang quadrangles to structurable algebras.

Provides new understanding of algebraic structures underlying these quadrangles.

Abstract

In 2000, J. Tits and R. Weiss classified all Moufang spherical buildings of rank two, also known as Moufang polygons. The hardest case in the classification consists of the Moufang quadrangles. They fall into different families, each of which can be described by an appropriate algebraic structure. For the exceptional quadrangles, this description is intricate and involves many different maps that are defined ad hoc and lack a proper explanation. In this paper, we relate these algebraic structures to two other classes of algebraic structures that had already been studied before, namely to Freudenthal triple systems and to structurable algebras. We show that these structures give new insight in the understanding of the corresponding Moufang quadrangles.