Automorphism groups of pure integral octonions

Mehmet Koca, Ramazan Koç

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2429-2442
Number of pages14
JournalJournal of Physics A: Mathematical and General
Volume27
Issue number7
DOIs
Publication statusPublished - Apr 7 1994

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Octonions
Root System
Automorphism Group
Physics
Order of a group
Chevalley Groups
Maximal Subgroup
Matrix Representation
subgroups
Roots
Subgroup
physics
matrices

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Physics A: Mathematical and General, Vol. 27, No. 7, 07.04.1994, p. 2429-2442.

Research output: Contribution to journalArticle

Koca, Mehmet ; Koç, Ramazan. / Automorphism groups of pure integral octonions. In: Journal of Physics A: Mathematical and General. 1994 ; Vol. 27, No. 7. pp. 2429-2442.
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