The Tenfold Way

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.

HEP - theorymathematical physicsgeneral mathematicsgroup theoryoperator algebrasquantum algebrarings and algebrasrepresentation theoryquantum physics

Audience: researchers in the discipline

Algebra, Particles, and Quantum theory

Series comments: An online series of talks on Algebra, Particles, and Quantum theory. You are more than welcome to join in at any point.