Advances in Mathematical Physics
Volume 2009 (2009), Article ID 483079, 11 pages
Rotations in the Space of Split Octonions
1Particle Physics Department, Andronikashvili Institute of Physics, 6 Tamarashvili Street, 0177 Tbilisi, Georgia
2Department of Physics, Faculty of Exact and Natural Sciences, Javakhishvili Tbilisi State University, 3 Chavchavadze Avenue, 0128 Tbilisi, Georgia
3Department of Physics, California State University, 2345 E. San Ramon Avenue, M/S MH37, Fresno, CA 93740, USA
Received 27 March 2009; Accepted 11 May 2009
Academic Editor: Fedele Lizzi
Copyright © 2009 Merab Gogberashvili. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 , while active rotations are done by the direct product of -boosts and real noncompact form of the exceptional group . In classical limit, these transformations reduce to the standard Lorentz group.