An octonionic construction of $E_8$ and the Lie algebra magic square
We give a new construction of the Lie algebra of type $E_8$, in terms of $3\times3$ matrices, such that the Lie bracket has a natural description as the matrix commutator. This leads to a new interpretation of the Freudenthal-Tits magic square of Lie algebras, acting on themselves by commutation.
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