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

 

Reconstruction of path algebras from their posets of tilting modules


Authors: Dieter Happel and Luise Unger
Journal: Trans. Amer. Math. Soc. 361 (2009), 3633-3660
MSC (2000): Primary 16G10, 16G70, 16E10
Published electronically: February 4, 2009
MathSciNet review: 2491894
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Abstract: Let $ \Lambda = k \overrightarrow{\Delta}$ be the path algebra of a finite quiver without oriented cycles. The set of isomorphism classes of multiplicity free tilting modules is in a natural way a partially ordered set. We will show here that $ \mathcal T_{\Lambda}$ uniquely determines $ \overrightarrow{\Delta}$ if $ \overrightarrow{\Delta}$ has no multiple arrows and no isolated vertices.


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Additional Information

Dieter Happel
Affiliation: Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
Email: happel@mathematik.tu-chemnitz.de

Luise Unger
Affiliation: Fakultät für Mathematik und Informatik, Fernuniversität Hagen, D-58084 Hagen, Germany
Email: luise.unger@fernuni-hagen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04644-3
PII: S 0002-9947(09)04644-3
Received by editor(s): April 16, 2007
Published electronically: February 4, 2009
Additional Notes: The main results presented here were obtained while the authors were visiting the University of Sao Paulo and Shanghai Jiao Tong University. Both authors would like to thank their hosts Flavio Coelho and Pu Zhang for their hospitality.
Article copyright: © Copyright 2009 American Mathematical Society