A trip around octonions

Abstract

In these expository notes, after a contemplation on the dawn of octonions, we give proofs for the Frobenius theorem and the Hurwitz theorem, we review the basics of Clifford algebras and spin groups, and exemplify the startling role played by the octonions in 7- A nd 8-dimensional phenomena such as the special 3- A nd 4-forms, the Bonan form, Spin(7) and Spin(8) groups and the mysterious triality.