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Minimal representation-infinite coil algebras

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Abstract

For a basic and connected finite dimensional algebra A over an algebraically closed field, we study when the cycles in the category mod A (of finite dimensional modules) are well-behaved. We call A cycle-finite if, for any cycle in mod A, no morphism on the cycle lies in the infinite power of the radical. We show that, in this case, A is tame. We also introduce a natural generalisation of a tube, called a coil, and define A to be a coil algebra if any cycle in mod A lies in a standard coil. We prove that the minimal representation-infinite coil algebras coincide with the tame concealed algebras.

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Authors and Affiliations

  1. Département de mathématiques et d’informatique, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada

    Ibrahim Assem

  2. Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100, Toruń, Poland

    Andrzej Skowroński

Authors
  1. Ibrahim Assem
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  2. Andrzej Skowroński
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Assem, I., Skowroński, A. Minimal representation-infinite coil algebras. Manuscripta Math 67, 305–331 (1990). https://doi.org/10.1007/BF02568435

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