Quaternionic Lorentz group and Dirac equation

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