Cluster algebras and preprojective algebras : the non simply-laced case

We generalize to the non simply-laced case results of Gei\ss, Leclerc and Schr"oer about the cluster structure of the coordinate ring of the maximal unipotent subgroups of simple Lie groups. In this way, cluster structures in the non simply-laced case can be seen as projections of cluster structures in the simply-laced case. This allows us to prove that cluster monomials are linearly independent in the non simply-laced case.