Rotations in the Space of Split Octonions

The geometrical application of split octonions is considered. The new representation of products of the basis units of split octonionic having David's star shape (instead of the Fano triangle) is presented. It is shown that active and passive transformations of coordinates in octonionic “eight-...

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Main Author: Merab Gogberashvili
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2009/483079
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author Merab Gogberashvili
author_facet Merab Gogberashvili
author_sort Merab Gogberashvili
collection DOAJ
description The geometrical application of split octonions is considered. The new representation of products of the basis units of split octonionic having David's star shape (instead of the Fano triangle) is presented. It is shown that active and passive transformations of coordinates in octonionic “eight-space” are not equivalent. The group of passive transformations that leave invariant the pseudonorm of split octonions is SO(4,4), while active rotations are done by the direct product of O(3,4)-boosts and real noncompact form of the exceptional group G2. In classical limit, these transformations reduce to the standard Lorentz group.
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spelling doaj-art-d706ae2745bd42f286972d11a52e540e2025-02-03T06:47:23ZengWileyAdvances in Mathematical Physics1687-91201687-91392009-01-01200910.1155/2009/483079483079Rotations in the Space of Split OctonionsMerab Gogberashvili0Particle Physics Department, Andronikashvili Institute of Physics, 6 Tamarashvili Street, 0177 Tbilisi, GeorgiaThe geometrical application of split octonions is considered. The new representation of products of the basis units of split octonionic having David's star shape (instead of the Fano triangle) is presented. It is shown that active and passive transformations of coordinates in octonionic “eight-space” are not equivalent. The group of passive transformations that leave invariant the pseudonorm of split octonions is SO(4,4), while active rotations are done by the direct product of O(3,4)-boosts and real noncompact form of the exceptional group G2. In classical limit, these transformations reduce to the standard Lorentz group.http://dx.doi.org/10.1155/2009/483079
spellingShingle Merab Gogberashvili
Rotations in the Space of Split Octonions
Advances in Mathematical Physics
title Rotations in the Space of Split Octonions
title_full Rotations in the Space of Split Octonions
title_fullStr Rotations in the Space of Split Octonions
title_full_unstemmed Rotations in the Space of Split Octonions
title_short Rotations in the Space of Split Octonions
title_sort rotations in the space of split octonions
url http://dx.doi.org/10.1155/2009/483079
work_keys_str_mv AT merabgogberashvili rotationsinthespaceofsplitoctonions