Open AccessA trip around octonions
Author(s) -
Ayşe Hümeyra Bilge,
Tekin Dereli,
Şahin Koçak
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2191/1/012006
Subject(s) - triality , mathematical proof , pure mathematics , contemplation , spin (aerodynamics) , mathematics , algebra over a field , theoretical physics , physics , philosophy , epistemology , geometry , thermodynamics
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 — and 8 —dimensional phenomena such as the special 3— and 4—forms, the Bonan form, Spin (7) and Spin (8) groups and the mysterious triality.