TY - JOUR A2 - Lizzi, Fedele AU - Gogberashvili, Merab PY - 2009 DA - 2009/07/01 TI - Rotations in the Space of Split Octonions SP - 483079 VL - 2009 AB - 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. SN - 1687-9120 UR - https://doi.org/10.1155/2009/483079 DO - 10.1155/2009/483079 JF - Advances in Mathematical Physics PB - Hindawi Publishing Corporation KW - ER -