Composition algebras and the two faces of $G_2$

Abstract

We consider composition and division algebras over the real numbers: We note two rôles for the group $G_2$: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams the relation between some pertinent groups, most of them related to the octonions. Some applications to physics are also discussed.

11 pages, 3 figures

References in corpus (2)

• M(ysterious) Patterns in SO(9)
• Arguments for F-theory

Cited by in corpus (1)

• Introduction to Sporadic Groups for physicists