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arXiv · 1711.07881

The Magic Star of Exceptional Periodicity

Piero Truini·Michael Rios·Alessio Marrani
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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.

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Piero Truini, Michael Rios, Alessio Marrani. 2017-11-21. The Magic Star of Exceptional Periodicity. https://doi.org/10.1090/conm%2F721

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