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.
M(ysterious) Patterns in SO(9)
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abstract
The light-cone little group, SO(9), classifies the massless degrees of freedom of eleven-dimensional supergravity, with a triplet of representations. We observe that this triplet generalizes to four-fold infinite families with the quantum numbers of massless higher spin states. Their mathematical structure stems from the three equivalent ways of embedding SO(9) into the exceptional group $F_4$.
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2019 1verdicts
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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.