Infinite dimensional Jordan algebras and symmetric cones

TL;DR

This paper extends the classical correspondence between finite dimensional Jordan algebras and symmetric cones to the infinite dimensional case, broadening the theoretical framework.

Contribution

It generalizes the Koecher-Vinberg correspondence to infinite dimensional Jordan algebras and symmetric cones.

Findings

Established a one-to-one correspondence in infinite dimensions

Extended finite dimensional theory to infinite-dimensional setting

Provided new insights into the structure of infinite dimensional Jordan algebras

Abstract

A celebrated result of Koecher and Vinberg asserts the one-one correspondence between the finite dimensional formally real Jordan algebras and Euclidean symmetric cones. We extend this result to the infinite dimensional setting.