Boya, Luis J.Campoamor Stursberg, Otto-Rudwig2023-06-202023-06-2020100219-887810.1142/S0219887810004348https://hdl.handle.net/20.500.14352/43761We 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.engjournal articlehttps//doi.org/10.1142/S0219887810004348http://www.worldscientific.com/doi/abs/10.1142/S0219887810004348open access512First exceptional Lie group G2Composition algebraDivision algebraOctonionsAutomorphism group of octonionsIsotropy groupQuaternionsSplit octonionsTensorsSpin groupsF4Álgebra1201 Álgebra