### 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 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*27*(7), 2429-2442. https://doi.org/10.1088/0305-4470/27/7/021

**Automorphism groups of pure integral octonions.** / Koca, Mehmet; Koç, Ramazan.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 27, no. 7, pp. 2429-2442. https://doi.org/10.1088/0305-4470/27/7/021

}

TY - JOUR

T1 - Automorphism groups of pure integral octonions

AU - Koca, Mehmet

AU - Koç, Ramazan

PY - 1994/4/7

Y1 - 1994/4/7

N2 - A matrix representation of the automorphism group of pure integral octonions constituting the root system of E7 is constructed. It is shown that it is a finite subgroup of the exceptional group of G2 of order 12096, called the adjoint Chevalley group G2(2). Its four maximal subgroups of orders 432, 192, 192′ and 336 preserve, respectively, the octonionic root systems of E6, SO(12), SU(2)3SO(8) and SU(8). It is also shown explicitly that the full automorphism group of the pure octonions ±et (i=1,⋯, 7) constituting the roots of SU(2)7 is a group of order 1344. Possible implications in physics are discussed.

AB - A matrix representation of the automorphism group of pure integral octonions constituting the root system of E7 is constructed. It is shown that it is a finite subgroup of the exceptional group of G2 of order 12096, called the adjoint Chevalley group G2(2). Its four maximal subgroups of orders 432, 192, 192′ and 336 preserve, respectively, the octonionic root systems of E6, SO(12), SU(2)3SO(8) and SU(8). It is also shown explicitly that the full automorphism group of the pure octonions ±et (i=1,⋯, 7) constituting the roots of SU(2)7 is a group of order 1344. Possible implications in physics are discussed.

UR - http://www.scopus.com/inward/record.url?scp=21344476046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344476046&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/27/7/021

DO - 10.1088/0305-4470/27/7/021

M3 - Article

AN - SCOPUS:21344476046

VL - 27

SP - 2429

EP - 2442

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 7

ER -