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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extension-orthogonal components of preprojective varieties


Authors: Christof Geiß and Jan Schröer
Journal: Trans. Amer. Math. Soc. 357 (2005), 1953-1962
MSC (2000): Primary 14M99, 16D70, 16G20, 17B37
Published electronically: August 11, 2004
MathSciNet review: 2115084
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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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Additional Information

Christof Geiß
Affiliation: Instituto de Matemáticas, UNAM, Ciudad Universitaria, 04510 Mexico D.F., Mexico
Email: christof@math.unam.mx

Jan Schröer
Affiliation: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
Email: jschroer@maths.leeds.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03555-X
PII: S 0002-9947(04)03555-X
Received by editor(s): September 5, 2002
Received by editor(s) in revised form: October 7, 2003
Published electronically: August 11, 2004
Additional Notes: The second author thanks the Nuffield Foundation (Grant Number NAL/00270/G) for financial support, and the IM UNAM, Mexico City, where most of this work was done
Article copyright: © Copyright 2004 American Mathematical Society