# Cyclic orders defined by ordered jordan algebras

## TL;DR

This paper introduces a new framework for partially ordered Jordan algebras, establishing a natural invariant partial cyclic order on their associated geometries, and outlines a research program to generalize classical symmetric cone theory.

## Contribution

It defines partially ordered Jordan algebras over rings and constructs a natural cyclic order on their geometries, extending classical symmetric cone and bounded domain theories.

## Key findings

- Invariant partial cyclic order on Jordan geometries
- Interval topology modeled on symmetric cones
- Framework for generalizing symmetric domain theory

## Abstract

We define a general notion of partially ordered Jordan algebra (over a partially ordered ring), and we show that the Jordan geometry associated to such a Jordan algebra admits a natural invariant partial cyclic order, whose intervals are modelled on the symmetric cone of the Jordan algebra. We define and describe, by affine images of intervals, the interval topology on the Jordan geometry, and we outline a reserch program aiming at generalizing main features of the theory of classical symmetric cones and bounded symmetric domains.