Boundary Moufang trees with abelian root groups of characteristic p

TL;DR

This paper proves that certain Moufang sets with abelian root groups associated with locally finite trees are derived from rank one simple algebraic groups over local fields, establishing a classification result.

Contribution

It establishes a classification of Moufang sets with abelian root groups in terms of algebraic groups over local fields.

Findings

Moufang sets with abelian root groups are linked to algebraic groups over local fields.

All such Moufang sets originate from rank one simple algebraic groups.

The result connects geometric group actions with algebraic structures.

Abstract

We prove that Moufang sets with abelian root groups arising at infinity of a locally finite tree all come from rank one simple algebraic groups over local fields.