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The new construction given by Barton and Sudbery of the Freudenthal-Tits magic square, which includes the exceptional classical simple Lie algebras, will be interpreted and extended by using a pair of symmetric composition algebras, instead of the standard unital composition algebras.
This is an account of some work of Markus Rost and his students Dominik Boos and Susanne Maurer. It concerns the possible dimensions for composition (also called Hurwitz) algebras. We adapt the work to the braided monoidal setting.
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