Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems

TL;DR

This paper explicitly classifies orbits of reducible Jordan algebras and Freudenthal triple systems, aiding the classification of extremal black hole solutions in certain supergravity theories.

Contribution

It provides explicit orbit representatives for reducible Jordan algebras and Freudenthal triple systems, linking algebraic classification to black hole solution categorization.

Findings

Explicit orbit representatives determined

Application to black hole solution classification

Enhanced understanding of algebraic structures in supergravity

Abstract

We determine explicit orbit representatives of reducible Jordan algebras and of their corresponding Freudenthal triple systems. This work has direct application to the classification of extremal black hole solutions of N = 2, 4 locally supersymmetric theories of gravity coupled to an arbitrary number of Abelian vector multiplets in D = 4, 5 space-time dimensions.