Octonions, Clifford algebras, spinors, triality & the exceptional Lie groups

Philip Arathoon

G.205,

We are all familiar with the real and complex numbers. Some of us are even comfortable with the quaternions, however very few of us have healthy relations with the octonions. The real numbers give rise to orthogonality, the complexes with Hermitian/unitary structures and the quaternions with "symplectic" structures, but what of the octonions? Hopefully if time (and careful planning) allow it we shall see a mysterious link between the octonions and the five exceptional Lie groups along with connections to triality and spinor representations. If however time does not allow it then at the very least I hope to say some nice things about the octonions.

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