Symmetries of the octonionic root system of E8

Mehmet Koca*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)497-510
Number of pages14
JournalJournal of Mathematical Physics
Issue number2
Publication statusPublished - 1992
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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