### Abstract

Octonionic root system of E_{8} is decomposed as the 9 sets of Hurwitz integers, each set satisfying the binary tetrahedral group structure, and the 12 sets of quaternionic units, each set obeying the dicylic group structure of order 12. This fact is used to prove that the automorphism group of the octonionic root system of E_{7} is the finite subgroup of G _{2}, of order 12 096, an explicit 7×7 matrix realization of which is constructed. Possible use of the octonionic representation of the E _{6} root system as orbifolds and the relevance of the binary tetrahedral structures with the statistical mechanics models are suggested.

Original language | English |
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Pages (from-to) | 497-510 |

Number of pages | 14 |

Journal | Journal of Mathematical Physics |

Volume | 33 |

Issue number | 2 |

Publication status | Published - 1992 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*33*(2), 497-510.

**Symmetries of the octonionic root system of E8
.** / Koca, Mehmet.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 33, no. 2, pp. 497-510.

}

TY - JOUR

T1 - Symmetries of the octonionic root system of E8

AU - Koca, Mehmet

PY - 1992

Y1 - 1992

N2 - Octonionic root system of E8 is decomposed as the 9 sets of Hurwitz integers, each set satisfying the binary tetrahedral group structure, and the 12 sets of quaternionic units, each set obeying the dicylic group structure of order 12. This fact is used to prove that the automorphism group of the octonionic root system of E7 is the finite subgroup of G 2, of order 12 096, an explicit 7×7 matrix realization of which is constructed. Possible use of the octonionic representation of the E 6 root system as orbifolds and the relevance of the binary tetrahedral structures with the statistical mechanics models are suggested.

AB - Octonionic root system of E8 is decomposed as the 9 sets of Hurwitz integers, each set satisfying the binary tetrahedral group structure, and the 12 sets of quaternionic units, each set obeying the dicylic group structure of order 12. This fact is used to prove that the automorphism group of the octonionic root system of E7 is the finite subgroup of G 2, of order 12 096, an explicit 7×7 matrix realization of which is constructed. Possible use of the octonionic representation of the E 6 root system as orbifolds and the relevance of the binary tetrahedral structures with the statistical mechanics models are suggested.

UR - http://www.scopus.com/inward/record.url?scp=33646431244&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646431244&partnerID=8YFLogxK

M3 - Article

VL - 33

SP - 497

EP - 510

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

ER -