In this paper, we propose the generalized description of electromagnetism and linear gravity based on the combined dual numbers and complex quaternion algebra. In this approach, the electromagnetic and gravitational fields can be considered as the components of one combined dual-complex quaternionic field. It is shown that all relations between potentials, field strengths and sources can be formulated in the form of compact quaternionic differential equations. The alternative reformulation of equations of gravitoelectromagnetism based on formalism of 8 × 8 matrices is also discussed. The results reveal the similarity and isomorphism of distinctive algebraic structures.

中文翻译：

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引力电磁学的双复四元数表示

在本文中，我们提出了基于组合对偶数和复四元数代数的电磁学和线性引力的广义描述。在这种方法中，电磁场和引力场可以被认为是一个组合的双复四元离子场的组成部分。结果表明，电位、场强和源之间的所有关系都可以用紧致四元微分方程的形式表示。基于形式主义的引力电磁方程的替代重构8 × 8矩阵也进行了讨论。结果揭示了独特代数结构的相似性和同构性。