The Extended Freudenthal Magic Square via Tensor Categories

Explore a 53-minute lecture on "The Extended Freudenthal Magic Square via tensor categories" presented by Alberto Elduque from the Universidad de Zaragoza at IPAM's Symmetric Tensor Categories and Representation Theory Workshop. Delve into the intricacies of nontrivial unital composition superalgebras in characteristic 3, derived from the split Cayley algebra and its order 3 automorphisms. Discover how these are obtained through the semisimplification process of the symmetric tensor category of representations of the cyclic group of order 3. Uncover a unified approach to deriving Lie superalgebras in the Extended Freudenthal Magic Square in characteristic 3 by "semisimplifying" the simple Lie algebra of type E8. Recorded on January 11, 2024, this talk offers advanced insights into algebraic structures and their connections to tensor categories and representation theory.