(2 + 1)-Maxwell Equations in Split Quaternions

The properties of spinors and vectors in (2 + 2) space split quaternions are studied. Quaternionic representation rotations naturally separates two SO(2,1) subgroups the full group symmetry norms quaternions, SO(2,2). One them represents symmetries three-dimensional Minkowski space-time. Then, second subgroup, generated by additional time-like coordinate from basis can be viewed as internal model. It is shown that analyticity condition, applying to invariant construction equivalent some system differential equations for quaternionic vectors. Assuming derivatives extra generate triality (supersymmetric) rotations, equation reduced exact Dirac–Maxwell