Local Moufang sets and local Jordan pairs

TL;DR

This paper explores the relationship between local Moufang sets and local Jordan pairs, establishing constructions that connect these algebraic structures and revealing their mutual correspondence under certain conditions.

Contribution

It introduces a method to construct local Moufang sets from local Jordan pairs and vice versa, highlighting a new duality between these structures.

Findings

Constructed local Moufang sets from every local Jordan pair.

Showed that certain local Moufang sets correspond to local Jordan pairs.

Explored the connections and conditions linking the two structures.

Abstract

In this paper, we extend the theory of special local Moufang sets. We construct a local Moufang set from every local Jordan pair, and we show that every local Moufang set satisfying certain (natural) conditions gives rise to a local Jordan pair. We also explore the connections between these two constructions.