Conformal Mappings, Hyperanalyticity and Field Dynamics

Generalization of complex analysis to the case of noncommutative algebras of a quaternion-like type is presented. There exists a correspondence between quaternion-differentiable functions and conformal mappings in Euclidean 4-space. For the algebra of biquaternions differentiability conditions are nonlinear and Lorentz-invariant. Starting from these, a version of algebraic field theory, algebrodynamics is suggested. Solutions of basic equations are obtained, and relations to the Maxwell theory disputed.