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Rotations in the Space of Split Octonions

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arxiv 0808.2496 v1 pith:3RPFMPPA submitted 2008-08-18 math-ph gr-qchep-thmath.MP

Merab Gogberashvili This is my paper · ORCID
classification math-phgr-qchep-thmath.MP
keywords splitgroupoctonionstransformationsactiveoctonionicpassiverotations
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abstract

The geometrical application of split octonions is considered. The modified Fano graphic, which represents products of the basis units of split octonionic, having David's Star shape, is presented. It is shown that active and passive transformations of coordinates in octonionic '8-space' are not equivalent. The group of passive transformations that leave invariant the norm of split octonions is SO(4,4), while active rotations is done by the direct product of O(3,4)-boosts and real non-compact form of the exceptional group $G_2$. In classical limit these transformations reduce to the standard Lorentz group.

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  1. The Dirac equation in (split-)octonions: origins, variants, and modern context

    math-ph 2026-06 conditional novelty 5.0 of 10

    Four approaches to the Dirac equation in (split-)octonions are classified; a 2024 split-octonionic equation is shown identical to the 2006 2-factor form by structure-preserving rotation and relabeling.

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