arXiv subjects

Christof Geiß

Publications and source records attributed to Christof Geiß.

20 records · Page 2Linked to original sources

arXiv2006

Rigid modules over preprojective algebras

Let $\la$ be a preprojective algebra of simply laced Dynkin type $Δ$. 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 $Δ$. As an application we obtain that all cluster monomials of $\C[N]$ belong to the dual semicanonical basis.

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arXiv2002

Extension-orthogonal components of nilpotent varieties

Let Q be a Dynkin quiver, and let P(Q) be the corresponding preprojective algebra. Let I be a set of pairwise different indecomposable irreducible components of varieties of P(Q)-modules such that generically there are no extensions between these components. We show that the number of elements in I is at most the number of positive roots of Q. Furthermore, we give a module theoretic interpretation of Leclerc's counterexample to a conjecture of Berenstein and Zelevinsky.

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