Capi Corrales (Madrid) <BR><BR>

<i>On the group of units of an order
in a non-split quaternion algebra</i>

<BR><BR>

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 $K=\QQ(\sqrt{-7})$.