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ON THE CLASSIFICATION OF FOUR-DIMENSIONAL MÖBIUS TRANSFORMATIONS
Published online by Cambridge University Press: 09 February 2007
Abstract
Based on the identification of four-dimensional Möbius transformations
$$ g(x)=(ax+b)(cx+d)^{-1} $$
by the matrix group $\mathrm{PS}_\triangle L(2,\mathbb{H})$ of quaternionic $2\times2$ matrices with Dieudonné determinant equal to $1$, we give an explicit expression for the classification of $g$ in terms of $a$, $b$, $c$ and $d$.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 1 , February 2007 , pp. 49 - 62
- Copyright
- Copyright © Edinburgh Mathematical Society 2007
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