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Rigid modules over preprojective algebras

Christof Geiß·Bernard Leclerc·Jan Schröer
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Abstract

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.

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Christof Geiß, Bernard Leclerc, Jan Schröer. 2005-03-16. Rigid modules over preprojective algebras. https://doi.org/10.1007/s00222-006-0507-y

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