Rigid modules over preprojective algebras

Details Rigid modules over preprojective algebras Rigid modules over preprojective algebras

2005-03-16

arxiv.org/abs/math/0503324v3

Mathematics

Representation Theory

34 pages. Final Version.To appear in Invent. Math. Minor changes

Scientific paper

10.1007/s00222-006-0507-y

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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