Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems

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.

18 pages. Updated to match published version

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• Black holes and general Freudenthal transformations
• Real weights, bound states and duality orbits
• Sextonions, Zorn Matrices, and ${\mathbf{e}}_{7\frac{1}{2}}$
• Albert algebras over Z and other rings
• Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity
• Qubit entanglement: A Jordan algebraic perspective