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Large tilting modules and representation type

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Abstract

We study finiteness conditions on large tilting modules over arbitrary rings. We then turn to a hereditary artin algebra R and apply our results to the (infinite dimensional) tilting module L that generates all modules without preprojective direct summands. We show that the behaviour of L over its endomorphism ring determines the representation type of R. A similar result holds true for the (infinite dimensional) tilting module W that generates the divisible modules. Finally, we extend to the wild case some results on Baer modules and torsion-free modules proven in Angeleri Hügel, L., Herbera, D., Trlifaj, J.: Baer and Mittag-Leffler modules over tame hereditary algebras. Math. Z. 265, 1–19 (2010) for tame hereditary algebras.

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Authors and Affiliations

  1. Dipartimento di Informatica—Settore di Matematica, Università degli Studi di Verona, Strada le Grazie 15-Ca Vignal, 37134, Verona, Italy

    Lidia Angeleri Hügel

  2. Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany

    Otto Kerner

  3. Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Prague 8, Czech Republic

    Jan Trlifaj

Authors
  1. Lidia Angeleri Hügel
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  2. Otto Kerner
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  3. Jan Trlifaj
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Correspondence to Otto Kerner.

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Angeleri Hügel, L., Kerner, O. & Trlifaj, J. Large tilting modules and representation type. manuscripta math. 132, 483–499 (2010). https://doi.org/10.1007/s00229-010-0356-2

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  • DOI: https://doi.org/10.1007/s00229-010-0356-2

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