On the group of units of an order in a non-split quaternion algebra

In this talk we will reflect on the group of units of an order in a non-split quaternion algebra with coefficients in a number field $K$. First we will study this group in general through the action of its elements of norm 1 on the three dimensional hyperbolic space, and then we will look at the case of imaginary quadratic fields. We will finally consider the case $K=\QQ(\sqrt{-7})$.