Rotations in the Space of Split Octonions

Details Rotations in the Space of Split Octonions Rotations in the Space of Split Octonions

2008-08-18

arxiv.org/abs/0808.2496v1

Advances in Mathematical Physics, vol. 2009, 483079 (2009).

Physics

Mathematical Physics

10 pages, 1 figure

Scientific paper

10.1155/2009/483079

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.

Affiliated with

Also associated with

No associations

Rating

Rotations in the Space of Split Octonions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rotations in the Space of Split Octonions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rotations in the Space of Split Octonions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-131651