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Article Dans Une Revue Inventiones Mathematicae Année : 2006

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.

Dates et versions

hal-00005707 , version 1 (29-06-2005)

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Christof Geiss, Bernard Leclerc, Jan Schröer. Rigid modules over preprojective algebras. Inventiones Mathematicae, 2006, 165, pp.589-632. ⟨hal-00005707⟩
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