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00925njm 22002777a 4500 dc Boya, Luis J. author Campoamor Stursberg, Otto-Rudwig author 2010 We consider composition and division algebras over the real numbers: We note two roles for the group G2: 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. 0219-8878 10.1142/S0219887810004348 https://hdl.handle.net/20.500.14352/43761 https//doi.org/10.1142/S0219887810004348 http://www.worldscientific.com/doi/abs/10.1142/S0219887810004348 Composition algebras and the two faces of G2