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Braid Groups pp 311-314 | Cite as

Presentations of SL2(Z) and PSL2(Z)

  • Christian Kassel
  • Vladimir Turaev
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 247)

Let \(\textrm{SL}_2({\bf Z})\) be the group of \(2 \times 2\) matrices with entries in \({\bf Z}\) and with determinant 1. The center of \(\textrm{SL}_2({\bf Z})\) is the group of order 2 generated by the scalar matrix \(-I_2\), where I 2 is the unit matrix. The quotient group
$$\textrm{PSL}_2({\bf Z}) = \textrm{SL}_2({\bf Z})/\langle -I_2 \rangle$$
is called the modular group; it can be identified with the group of rational functions on \({\bf C}\) of the form \((az+b)/(cz+d)\), where a, b, c, d are integers such that \(ad - bc = 1\).

Keywords

Rational Function Unit Matrix Group Theory Algebraic Structure Cell Complex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique Avancée, CNRS et Université Louis PasteurStrasbourgFrance
  2. 2.Department of MathematicsIndiana University BloomingtonBloomingtonUSA

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