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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Constructing tilting modules
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by Otto Kerner and Jan Trlifaj PDF
Trans. Amer. Math. Soc. 360 (2008), 1907-1925 Request permission

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
  • MR Author ID: 194039
  • Jan Trlifaj
  • Affiliation: Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
  • MR Author ID: 174420
  • ORCID: 0000-0001-5773-8661
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 1907-1925
  • MSC (2000): Primary 16E30, 16G10, 16G30; Secondary 16D50, 18E40
  • DOI: https://doi.org/10.1090/S0002-9947-07-04392-9
  • MathSciNet review: 2366968