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

   

 

Generalized associahedra via quiver representations


Authors: Robert Marsh, Markus Reineke and Andrei Zelevinsky
Journal: Trans. Amer. Math. Soc. 355 (2003), 4171-4186
MSC (2000): Primary 52B11, 16G20, 17B20; Secondary 17B37, 05E99
Published electronically: June 10, 2003
MathSciNet review: 1990581
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Abstract | References | Similar Articles | Additional Information

Abstract: We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. The main properties of these fans then become easy consequences of the known facts about tilting modules due to K. Bongartz, D. Happel and C. M. Ringel.


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Additional Information

Robert Marsh
Affiliation: Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, England
Email: R.Marsh@mcs.le.ac.uk

Markus Reineke
Affiliation: BUGH Wuppertal, Gaußstraße 20, D-42097 Wuppertal, Germany
Email: reineke@math.uni-wuppertal.de

Andrei Zelevinsky
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email: andrei@neu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03320-8
PII: S 0002-9947(03)03320-8
Received by editor(s): May 26, 2002
Received by editor(s) in revised form: February 8, 2003
Published electronically: June 10, 2003
Additional Notes: Andrei Zelevinsky’s research was supported in part by NSF grants #DMS-9971362 and DMS-0200299. Robert Marsh’s research was supported in part by EPSRC grant GR/R17546/01. All authors were supported in part by a University of Leicester Research Fund Grant
Article copyright: © Copyright 2003 by Robert Marsh, Markus Reineke, and Andrei Zelevinsky