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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Gongopadhyay, Krishnendu 2012. Algebraic Characterization of Isometries of the Hyperbolic 4-Space. ISRN Geometry, Vol. 2012, p. 1.


    Gongopadhyay, Krishnendu 2010. Algebraic characterization of the isometries of the hyperbolic 5-space. Geometriae Dedicata, Vol. 144, Issue. 1, p. 157.


    Jakobs, Wencke and Krieg, Aloys 2010. Möbius transformations on ℝ3. Complex Variables and Elliptic Equations, Vol. 55, Issue. 4, p. 375.


    Parker, John R. and Short, Ian 2009. Conjugacy Classification of Quaternionic Möbius Transformations. Computational Methods and Function Theory, Vol. 9, Issue. 1, p. 13.


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  • Proceedings of the Edinburgh Mathematical Society, Volume 50, Issue 1
  • February 2007, pp. 49-62

ON THE CLASSIFICATION OF FOUR-DIMENSIONAL MÖBIUS TRANSFORMATIONS

  • Wensheng Cao (a1) (a2)
  • DOI: http://dx.doi.org/10.1017/S0013091505000398
  • Published online: 01 February 2007
Abstract
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 $d$.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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