Recently Karzel and Taherian introduced the concept of a group with collinearity \((G, \kappa )\) and showed that for \(\alpha \in G \) the maps

$$\begin{aligned} {{\tilde{\alpha }}}{:} \ G \rightarrow G ;~ \xi \mapsto \alpha \cdot \xi ^{-1} \cdot \alpha \end{aligned}$$

of the corresponding reflection structure \((G , {\widetilde{G}} )\), where \( {\tilde{G}} := \{{{\tilde{\gamma }}} \ | \ \gamma \in G \}\) are point reflections. We give here a new class of groups with collinearity. This class comes from the kinematic algebra of \(2\times 2\)-matrices.

中文翻译：

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具有共线性的组的例子

最近Karzel和Taherian引入了共线性的基团的概念\（（G，\卡帕）\） ，并表明对于\（\阿尔法\ G中\）的地图

$$ \ begin {aligned} {{\ tilde {\ alpha}}} {：} \ G \ rightarrow G;〜\ xi \ mapsto \ alpha \ cdot \ xi ^ {-1} \ cdot \ alpha \ end {aligned } $$

反射结构\（（G，{\ widetilde {G}}）\）的位置，其中\（{\ tilde {G}}：= \ {{{\ tilde {\ gamma}}} \ in G \} \）是点反射。我们在这里给一类新的具有共线性的组。此类来自\（2 × 2）矩阵的运动代数。