On Lorentz transformations with elliptic biquaternions

Z. Derin, M. A. Güngör

In this study, the Lorentz transformations which are in accordant with special relativity have been examined for the first time with elliptic biquaternions. Since the elliptic biquaternions contain the complex structure, it is beneficial to examine the Lorentz transformations which can be the building blocks of relativistic physics via elliptic biquaternions. Therefore, as a result of relativistic transformation relation, it has been seen that the Lorentz transformations can be expressed with elliptic biquaternions and some special results have been given. In addition, matrix representations of obtained mathematical expressions are given. Thanks to the matrix representations of elliptical biquaternions, the property of commutativeness which is not valid for elliptic biquaternions has been eliminated and these representations provide a convenience for relativistic transformation relation. In this context, the presented method in this article is very useful. 

Tbilisi Mathematical Journal, Special Issue (IECMSA-2019), pp. 125-144