The algebrodynamics: in search of the ultimate algebraic “world” structure

Principles of the so-called algebrodynamical approach to the construction of a unified field theory are presented, together with realization of the approach on the base of the linear algebra of complex quaternions. Then we discuss possible realizations of the algebrodynamics on a manifold equipped with the structure of a Lie group or its specific generalizations - algebraic structures (AS) defined by a single operation subject to a single relation containing three or four elements (analogous to the associativity requirement for a Lie group). Defined in such a way the so-called invariant AS turns out to be equivalent to a Lie group but allows thus for a non-canonical introduction of the latter which makes use of a single defining relation. The two more types of remarkable AS, the so-called automorphic and universal ones, are proposed for the role of the “World AS” and preliminary examined. Fundamental physical fields 𝐹(𝑥) are considered as nontrivial mappings of the elements of AS corresponding, in particular, to the multiplication of any element by itself, 𝐹(𝑥) = · 𝑥.