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ON THE CLASSIFICATION OF FOUR-DIMENSIONAL MÖBIUS TRANSFORMATIONS

Published online by Cambridge University Press:  09 February 2007

Wensheng Cao
Wensheng Cao
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China Institute of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China ([email protected])
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Abstract

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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 $d$.

Keywords

Primary 30F4022E4020H10quaternionfour-dimensional Möbius transformationsclassification
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