Split-Quaternion Analyticity and (2 + 1)-Electrodynamics

Abstract

It is shown that the analyticity condition, applying to the invariant construction of split quaternions, is equivalent to some system of differential equations for quaternionic spinors and vectors. Assuming that the derivatives by extra time-like coordinate of (2+2)-space of split quaternions generate triality (supersymmetric)rotations, the analyticity equations is reducedto the exact Dirac-Maxwell system in 3-dimensional Minkowski space-time.