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arXiv · 1005.3514

Jordan C*-Algebras and Supergravity

Michael Rios
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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.

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Michael Rios. 2010-05-19. Jordan C*-Algebras and Supergravity. https://arxiv.org/abs/1005.3514

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