Luis J. Boya, R. Campoamor-Stursberg. Composition algebras and the two faces of G_{2}
Natural Sciences / Physics / Mathematical Physics
Submitted on: Sep 12, 2012, 17:46:19
Description: We consider composition and division algebras over the real numbers: We note two roles 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.