The Extended Freudenthal Magic Square via tensor categories

Alberto Elduque
Universidad de Zaragoza

The nontrivial unital composition superalgebras, of dimension 3 and 6, which exist only in characteristic 3, are obtained from the split Cayley algebra and its order 3 automorphisms, by means of the process of semisimplification of the symmetric tensor category of representations of the cyclic group of order 3. This allows us to get, in a unified way, the Lie superalgebras in the Extended Freudenthal Magic Square in characteristic 3, by "semisimplifying" the simple Lie algebra of type E8.

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