  Let $\la$ be a preprojective algebra of simply laced Dynkin type $\Delta$. We
study maximal rigid $\la$-modules, their endomorphism algebras and a mutation
operation on these modules. This leads to a representation-theoretic
construction of the cluster algebra structure on the ring $\C[N]$ of polynomial
functions on a maximal unipotent subgroup $N$ of a complex Lie group of type
$\Delta$. As an application we obtain that all cluster monomials of $\C[N]$
belong to the dual semicanonical basis.
