John Baez - The Tenfold Way скачать в хорошем качестве

John Baez - The Tenfold Way

Talk given on the 6th of February 2023 for the Algebra, Particles, and Quantum Theory seminar series. Organized by Nichol (Cohl) Furey, Humboldt-Universität zu Berlin Abstract: The importance of the tenfold way in physics was only recognized in this century. Simply put, it implies that there are ten fundamentally different kinds of matter. But it goes back to 1964, when the topologist C. T. C. Wall classified the associative real super division algebras and found ten of them. The three "purely even" examples were already familiar: the real numbers, complex numbers and quaternions. The rest become important when we classify representations of groups or supergroups on Z/2-graded vector spaces. We explain this classification, its connection to Clifford algebras, and some of its implications. For more seminars go to https://furey.space