Split-octonion
In mathematics, the split-octonions are a nonassociative extension of the quaternions (or the split-quaternions). They differ from the octonions in the signature of quadratic form: the split-octonions have a split-signature (4,4) whereas the octonions have a positive-definite signature (8,0).
The split-octonions form the unique split octonion algebra over the real numbers. There are corresponding algebras over any field F.
Read more about Split-octonion: Properties, Zorn's Vector-matrix Algebra, Applications