Special Moufang sets of finite dimension

TL;DR

This paper establishes a connection between special Moufang sets with abelian root subgroups and quadratic Jordan division algebras under a finiteness condition, expanding understanding of their algebraic structure.

Contribution

It demonstrates that such Moufang sets originate from quadratic Jordan division algebras when specific finiteness criteria are met, revealing a new structural link.

Findings

Moufang sets with abelian root subgroups relate to quadratic Jordan division algebras

A finiteness condition ensures the derivation from quadratic Jordan algebras

Provides a classification framework for certain Moufang sets

Abstract

We prove that a special Moufang sets with abelian root subgroups derive from a quadratic Jordan division algebra if a certain finiteness condition is satisfied.