Quaternions and Special Relativity

We reformulate Special Relativity by a quaternionic algebra on reals. Using {\em real linear quaternions}, we show that previous difficulties, concerning the appropriate transformations on the $3+1$ space-time, may be overcome. This implies that a complexified quaternionic version of Special Relativity is a choice and not a necessity.Comment: 17 pages, latex, no figure

Octonionic Representations of GL(8,R) and GL(4,C)

Octonionic algebra being nonassociative is difficult to manipulate. We introduce left-right octonionic barred operators which enable us to reproduce the associative GL(8,R) group. Extracting the basis of GL(4,C), we establish an interesting connection between the structure of left-right octonionic barred operators and generic 4x4 complex matrices. As an application we give an octonionic representation of the 4-dimensional Clifford algebra.Comment: 14 pages, Revtex, J. Math. Phys. (submitted