Computing a Generating Set of Arithmetic Kleinian Groups

Details Computing a Generating Set of Arithmetic Kleinian Groups Computing a Generating Set of Arithmetic Kleinian Groups

2008-06-03

arxiv.org/abs/0806.0661v1

Mathematics

Numerical Analysis

Scientific paper

The goal of this paper is to demonstrate the use of techniques from hyperbolic geometry to compute generating sets of certain subgroups of $SL^+(2,\mathbb{C})$; specifically, $SO^+(Q,\mathbb{Z})$ for $Q$ some integral quadratic form of signature $(3,1)$ that does not represent 0. The algorithm is illustrated for the form $Q_7=x_1^2+x_2^2+x_3-7x^4$, and explicit generating matrices are found.

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