104 Yefremov A. P. Quaternions: algebra, geometry and physical theories QUATERNIONS: ALGEBRA, GEOMETRY AND PHYSICAL THEORIES

A review of modern study of algebraic, geometric and differential properties of quater-nionic (Q) numbers with their applications. Traditional and ”tensor ” formulation of Q-units with their possible representations are discussed and groups of Q-units transformations leaving Q-multiplication rule form-invariant are determined. A series of mathematical and physical applications is offered, among them use of Q-triads as a moveable frame, analysis of Q-spaces families, Q-formulation of Newtonian mechanics in arbitrary rotating frames, and realization of a Q-Relativity model comprising all effects of Special Relativity and admitting description of kinematics of non-inertial motion. A list of ”Quaternionic Coincidences ” is presented revealing surprising interconnection between basic relations of some physical theories and Q-numbers mathematics