Extension-orthogonal components of preprojective varieties

Geiß, Christof; Schröer, Jan

doi:10.1090/S0002-9947-04-03555-X

Extension-orthogonal components of preprojective varieties
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by Christof Geiß and Jan Schröer PDF

Trans. Amer. Math. Soc. 357 (2005), 1953-1962 Request permission

Abstract:

Let $Q$ be a Dynkin quiver, and let $\Lambda$ be the corresponding preprojective algebra. Let ${\mathcal C} = \{ C_i \mid i \in I \}$ be a set of pairwise different indecomposable irreducible components of varieties of $\Lambda$-modules such that generically there are no extensions between $C_i$ and $C_j$ for all $i,j$. We show that the number of elements in ${\mathcal C}$ 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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