The aim of this paper is to analyze and prove different facts related with bicomplex Möbius transformations. Various algebraic and geometric results were obtained, using the decomposition of the bicomplex set as: \({{\mathbb {B}}}{{\mathbb {C}}}= {{\mathbb {D}}}+ \textbf{i}{{\mathbb {D}}}\), and there were used actively both, hyperbolic and bicomplex, geometric objects. The basics of bicomplex Lobachevsky’s geometry are given.

中文翻译：

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有关双复莫比乌斯变换的更多信息：几何、代数和分析方面

本文的目的是分析和证明与双复莫比乌斯变换相关的不同事实。使用双复集的分解，获得了各种代数和几何结果： \({{\mathbb {B}}}{{\mathbb {C}}}= {{\mathbb {D}}}+ \textbf {i}{{\mathbb {D}}}\)，并且双曲线和双复形几何对象都被积极使用。给出了双复罗巴切夫斯基几何的基础知识。