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The Magic Star of Exceptional Periodicity
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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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Exceptional Periodicity and Magic Star Algebras. I : Foundations
The paper rigorously defines 'Magic Star algebras', periodic finite dimensional generalizations of e6, e7, and e8, which are Lie algebras only at the base level n=1.
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