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Traces, Cross-Ratios and 2-Generator Subgroups of SU(2, 1)

Published online by Cambridge University Press:  20 November 2018

Pierre Will
Pierre Will*
Affiliation:
Institut Fourier, 100 rue des Maths, 38402 StMartin d’Hères, France email: pierre.will@ujf-grenoble.fr
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Abstract

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In this work, we investigate how to decompose a pair $\left( A,\,B \right)$ of loxodromic isometries of the complex hyperbolic plane $\mathbf{H}_{\mathbb{C}}^{2}$ under the form $A\,=\,{{I}_{1}}{{I}_{2}}$ and $B\,=\,{{I}_{3}}{{I}_{2}}$, where the ${{I}_{k}}$'s are involutions. The main result is a decomposability criterion, which is expressed in terms of traces of elements of the group $\left\langle A,\,B \right\rangle $.

Keywords

14L2422E4032M1551M10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 6 , 01 December 2009 , pp. 1407 - 1436
Copyright
Copyright © Canadian Mathematical Society 2009

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