  Spaces with a Weyl-type connection and torsion of a special type induced by
the structure of the differentiability conditions in the algebra of complex
quaternions are considered. The consistency of these conditions implies the
self-duality of curvature. The Maxwell and SL(2, C) Yang-Mills fields
associated with the irreducible components of the connection also turn out to
be self-dual, so that the corresponding equations are fulfilled on the
solutions of the generating system. Using the twistor structure of the latter,
its general solution is obtained. The singular locus has a string-like
(particle-like) structure and generates the self-consistent algebraic dynamics
of the string system.
