Rotations in the Space of Split Octonions

Abstract EN

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.