Conformal Groups and Vahlen Matrices

Jacques Helmstetter, Universite Grenoble I, France

This article recalls some facts about the conformal group Conf(V,Q) of a quadratic space (V,Q); in particular there is a surjective group morphism O(V',Q')$\rightarrow$Conf(V,Q), where (V',Q') is the orthogonal sum of (V,Q) and a hyperbolic plane; its kernel is a group of order two. Then it explains how the elements of O(V',Q') and Conf(V,Q) can be represented by Vahlen matrices. And finally, it recalls some properties of Vahlen matrices.