Rigid modules over preprojective algebras
Résumé
Let $\lambda$ be a preprojective algebra of simply laced Dynkin type $\Delta$. We study maximal rigid $\lambda$-modules 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.