Automorphism groups of pure integral octonions

M. Koca; R. Koc

doi:10.1088/0305-4470/27/7/021

Automorphism groups of pure integral octonions

M. Koca^*, R. Koc

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 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)³*SO(8) and SU(8). It is also shown explicitly that the full automorphism group of the pure octonions +or-e_i (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
Article number	021
Pages (from-to)	2429-2442
Number of pages	14
Journal	Journal of Physics A: General Physics
Volume	27
Issue number	7
DOIs	https://doi.org/10.1088/0305-4470/27/7/021
Publication status	Published - 1994
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
General Physics and Astronomy
Mathematical Physics

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10.1088/0305-4470/27/7/021

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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)3*SO(8) and SU(8). It is also shown explicitly that the full automorphism group of the pure octonions +or-ei (i=1,..., 7) constituting the roots of SU(2)7 is a group of order 1344. Possible implications in physics are discussed.",

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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)3*SO(8) and SU(8). It is also shown explicitly that the full automorphism group of the pure octonions +or-ei (i=1,..., 7) constituting the roots of SU(2)7 is a group of order 1344. Possible implications in physics are discussed.

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Automorphism groups of pure integral octonions

Abstract

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