### Abstract

A matrix representation of the automorphism group of pure integral octonions constituting the root system of E_{7} is constructed. It is shown that it is a finite subgroup of the exceptional group of G_{2} of order 12096, called the adjoint Chevalley group G_{2}(2). Its four maximal subgroups of orders 432, 192, 192′ and 336 preserve, respectively, the octonionic root systems of E_{6}, SO(12), SU(2)^{3}SO(8) and SU(8). It is also shown explicitly that the full automorphism group of the pure octonions ±e_{t} (i=1,⋯, 7) constituting the roots of SU(2)^{7} is a group of order 1344. Possible implications in physics are discussed.

Original language | English |
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Pages (from-to) | 2429-2442 |

Number of pages | 14 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 27 |

Issue number | 7 |

DOIs | |

Publication status | Published - Apr 7 1994 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Koca, M., & Koç, R. (1994). Automorphism groups of pure integral octonions.

*Journal of Physics A: Mathematical and General*,*27*(7), 2429-2442. https://doi.org/10.1088/0305-4470/27/7/021