2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50587We 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.9 pages, AMS-TeXHigh Energy Physics - Theorytext