  We formulate Lorentz group representations in which ordinary complex numbers
are replaced by linear functions of real quaternions and introduce dotted and
undotted quaternionic one-dimensional spinors. To extend to parity the
space-time transformations, we combine these one-dimensional spinors into
bi-dimensional column vectors. From the transformation properties of the
two-component spinors, we derive a quaternionic chiral representation for the
space-time algebra. Finally, we obtain a quaternionic bi-dimensional version of
the Dirac equation.
