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four-dimensional möbius transformations

Proceedings of the Edinburgh Mathematical Society (1)

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ON THE CLASSIFICATION OF FOUR-DIMENSIONAL MÖBIUS TRANSFORMATIONS
Wensheng Cao
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 1 / February 2007

Published online by Cambridge University Press:

09 February 2007, pp. 49-62
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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 $d$.