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Length Categories of Infinite Height

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Geometric and Topological Aspects of the Representation Theory of Finite Groups (PSSW 2016)

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Abstract

For abelian length categories, the borderline between finite and infinite representation type is discussed. Characterisations of finite representation type are extended to length categories of infinite height, and the minimal length categories of infinite height are described.

Dedicated to Dave Benson on the occasion of his 60th birthday

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Notes

  1. 1.

    The proof of Theorem 4.10 is close to Butler’s original proof. Auslander’s proof is based on the use of a bilinear form on \(K_0(\mathcal C,0)\), following the work of Benson and Parker on Green rings [9].

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, D-33501, Bielefeld, Germany

    Henning Krause & Dieter Vossieck

Authors
  1. Henning Krause
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  2. Dieter Vossieck
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Correspondence to Henning Krause .

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Editors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, USA

    Jon F. Carlson

  2. Department of Mathematics, University of Utah, Salt Lake City, UT, USA

    Srikanth B. Iyengar

  3. Department of Mathematics, University of Washington, Seattle, WA, USA

    Julia Pevtsova

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Krause, H., Vossieck, D. (2018). Length Categories of Infinite Height. In: Carlson, J., Iyengar, S., Pevtsova, J. (eds) Geometric and Topological Aspects of the Representation Theory of Finite Groups. PSSW 2016. Springer Proceedings in Mathematics & Statistics, vol 242. Springer, Cham. https://doi.org/10.1007/978-3-319-94033-5_8

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