Transactions of the American Mathematical Society

Author(s): Otto Kerner; Jan Trlifaj
Journal: Trans. Amer. Math. Soc. 360 (2008), 1907-1925.
MSC (2000): Primary 16E30, 16G10, 16G30; Secondary 16D50, 18E40
Posted: October 30, 2007
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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

, we prove that for each $0 \leq i < n-1$ , there is an infinite dimensional tilting module

with exactly

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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 16E30, 16G10, 16G30, 16D50, 18E40

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: 10.1090/S0002-9947-07-04392-9
PII: S 0002-9947(07)04392-9
Received by editor(s): November 29, 2005
Posted: 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
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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