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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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2009/483079 |
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| _version_ | 1832546769629609984 |
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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. |
| format | Article |
| id | doaj-art-d706ae2745bd42f286972d11a52e540e |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| 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 |