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

 

Constructing tilting modules


Authors: Otto Kerner and Jan Trlifaj
Journal: Trans. Amer. Math. Soc. 360 (2008), 1907-1925
MSC (2000): Primary 16E30, 16G10, 16G30; Secondary 16D50, 18E40
Published electronically: October 30, 2007
MathSciNet review: 2366968
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Abstract: We investigate the structure of (infinite dimensional) tilting modules over hereditary artin algebras. For connected algebras of infinite representation type with Grothendieck group of rank $ n$, we prove that for each $ 0 \leq i < n-1$, there is an infinite dimensional tilting module $ T_i$ with exactly $ i$ pairwise non-isomorphic indecomposable finite dimensional direct summands. We also show that any stone is a direct summand in a tilting module. In the final section, we give explicit constructions of infinite dimensional tilting modules over iterated one-point extensions.


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Additional Information

Otto Kerner
Affiliation: Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstr.1, 40225 Düsseldorf, Germany

Jan Trlifaj
Affiliation: Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04392-9
PII: S 0002-9947(07)04392-9
Received by editor(s): November 29, 2005
Published electronically: October 30, 2007
Additional Notes: This research was done during visits of the first author to Charles University, Prague, and of the second author to Heinrich Heine University, Düsseldorf, within the bilateral university exchange program
The second author was supported by grants GAUK 448/2004/B-MAT and MSM 0021620839
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.