四元数与双四元数：代数、几何与物理理论
Quaternions and Biquaternions: Algebra, Geometry and Physical Theories
摘要：
综述了四元数的代数、几何和微分性质及其应用的现代研究。讨论了Q-单位的传统表述和“张量”表述及其可能的表示，确定了保持Q-乘法规则形式不变的Q-单位变换群。提供了一系列的数学和物理应用，其中包括使用Q-三元组作为一个可移动的框架，分析Q-空间家庭，Q-制定的牛顿力学在任意旋转框架，和实现的Q-相对论模型，包括所有的影响，狭义相对论和承认的运动学的非惯性运动的描述。一个“四元数巧合”的列表，揭示了一些物理理论和Q数数学的基本关系之间令人惊讶的互连。
英文摘要：
The review of modern study of algebraic, geometric and differential properties of quaternionic (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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
