Jordan C*-Algebras and Supergravity

Abstract

It is known that black hole charge vectors of N=8 and magic N=2 supergravity in four and five dimensions can be represented as elements of Jordan algebras of degree three over the octonions and split-octonions and their Freudenthal triple systems. We show both such Jordan algebras are contained in the exceptional Jordan C*-algebra and construct its corresponding Freudenthal triple system and single variable extension. The transformation groups for these structures give rise to the complex forms of the U-duality groups for N=8 and magic N=2 supergravities in three, four and five dimensions.

17 pages

References in corpus (10)

• Black holes admitting a Freudenthal dual
• Orbits and Attractors for N=2 Maxwell-Einstein Supergravity Theories in Five Dimensions
• Stringy Black Holes and the Geometry of Entanglement
• E_7 and the tripartite entanglement of seven qubits
• N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities
• E_6 and the bipartite entanglement of three qutrits
• Exceptional Projective Geometries and Internal Symmetries
• Jordan algebras, exceptional groups, and higher composition laws
• Jordan Algebras and Extremal Black Holes
• 4d-5d connection and the holomorphic anomaly