paper
The Octonions
John C. Baez
Use in this reference: Linked author-hosted paper. The group definitions and dimensions used here are factual summaries, not copied text.
Relevant material: Sections 4.1–4.6 on exceptional groups.
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| g₂ compact | Definition | Section 4.1: the Lie algebra of octonion derivations |
| g₂ compact | Definition | Section 4.1: octonion derivations |
| G₂ compact | Definition | Section 4.1: G₂ as octonion automorphisms |
| G₂ compact | Representation category and descent | Section 4.1: action on imaginary octonions and the subgroup G₂ ⊂ SO(7) |
| F₄ compact | Definition | Section 4.2: F₄ and the exceptional Jordan algebra |
| F₄ compact | Representation category and descent | Section 4.2: the 27-dimensional exceptional Jordan algebra and F₄ automorphisms |