Online Seminar: Algebra, Particles, and Quantum theory
Montag, 15. Mai 2023 // 19.00 - 20.30
Humboldt-Universität zu Berlin
The Algebra, Particles, and Quantum Theory international online seminar series is organized by Nichol Furey, a VW Stiftung Research Fellow in mathematical physics at Humboldt-Universität zu Berlin.
15 May 2023:
Symmetric spaces and the tenfold way
John Baez
U.C. Riverside
Abstract: The tenfold way has many manifestations. It began as a tenfold classification of states of matter based on their behavior under time reversal and charge conjugation. Mathematically, it relies on the fact that there are ten super division algebra and ten kinds of Clifford algebras, where two Clifford algebras are of the same kind if they have equivalent categories of representations. But Cartan also showed that there are ten infinite families of compact symmetric spaces! After explaining symmetric spaces, we describe two ways to get compact symmetric spaces from Clifford algebras, which give different correspondences between these two manifestations of the tenfold way.
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