Relativistic Algebra of Space-Time and Algebrodynamics

We consider a manifestly Lorentz invariant form $\mathbb L$ of the biquaternion algebra and its generalization to the case of curved manifold. The conditions of $\mathbb L$-differentiability of $\mathbb L$-functions are formulated and considered as the primary equations for fundamental fields modeled with such functions. The exact form of the effective affine connection induced by $\mathbb L$-differentiability equations is obtained for the flat and curved cases. In the flat case, the integrability conditions of the latter lead to the self-duality of the corresponding curvature, thus ensuring that the source-free Maxwell and $SL(2,\mathbb C)$ Yang-Mills equations hold on the solutions of the $\mathbb L$-differentiability equations