The Magic Star of Exceptional Periodicity

Abstract

We present a periodic infinite chain of finite generalisations of the exceptional structures, including e8, the exceptional Jordan algebra (and pair), and the octonions. We demonstrate that the exceptional Jordan algebra is part of an infinite family of finite-dimensional matrix algebras (corresponding to a particular class of cubic Vinberg's T-algebras). Correspondingly, we prove that e8 is part of an infinite family of algebras (dubbed "Magic Star" algebras) that resemble lattice vertex algebras.

arXiv comment1+18 pages, 5 figures; v2 : 1+22 pages, 5 figures; proofs of propositions added, some remarks in Secs. 1 and 7 added, Abstract modified, some typographic changes. Seminar delivered by Michael Rios at the 4th Mile High Conference on Nonassociative Mathematics University of Denver, Denver, Colorado, USA, July 29-August 5, 2017

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Cited by in corpus (8)

• A Twistorial Foundation for the Classical Double Copy
• Ehlers as EM duality in the double copy
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras
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