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Cycle-Finite Module Categories

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Algebras, Quivers and Representations

Part of the book series: Abel Symposia ((ABEL,volume 8))

Abstract

We describe the structure of module categories of finite dimensional algebras over an algebraically closed field for which the cycles of nonzero nonisomorphisms between indecomposable finite dimensional modules are finite (do not belong to the infinite Jacobson radical of the module category). Moreover, geometric and homological properties of these module categories are exhibited.

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Acknowledgements

The authors gratefully acknowledge supports from the grant No. DEC-2011/02/A/ST1/00216 of the Polish National Science Center and the Centro de Investigación en Mathemáticas (CIMAT) Guanajuato in México.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland

    Piotr Malicki & Andrzej Skowroński

  2. Centro de Investigación en Mathemáticas (CIMAT), Guanajuato, México

    José A. de la Peña

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  1. Piotr Malicki
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  2. José A. de la Peña
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  3. Andrzej Skowroński
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Correspondence to Piotr Malicki .

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Editors and Affiliations

  1. NTNU Dept. of Mathematical Sciences, Trondheim, Norway

    Aslak Bakke Buan

  2. NTNU Dept. of Mathematical Sciences, Trondheim, Norway

    Idun Reiten

  3. NTNU Dept. of Mathematical Sciences, Trondheim, Norway

    Øyvind Solberg

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Malicki, P., de la Peña, J.A., Skowroński, A. (2013). Cycle-Finite Module Categories. In: Buan, A., Reiten, I., Solberg, Ø. (eds) Algebras, Quivers and Representations. Abel Symposia, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39485-0_10

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