  Let \Gamma be a Dynkin diagram of type A,D,E and let R denote the
corresponding root system. In this paper we give a categorical construction of
R from \Gamma. Instead of choosing an orientation of \Gamma and studying
representations of the associated quiver, we study representations of a
canonical quiver \Gammahat associated to \Gamma . This construction is very
closely related to the preprojective algebra of \Gamma . In particular, the
construction gives a certain periodicity result about the preprojective
algebra.
