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Existence of cycle-finite algebras of infinite representation type without directing projective or injective modules

Volume 148 / 2017

Piotr Malicki, José Antonio de la Peña, Andrzej Skowroński Colloquium Mathematicum 148 (2017), 165-190 MSC: Primary 16G10, 16G70; Secondary 16G60. DOI: 10.4064/cm7190-2-2017 Published online: 24 April 2017

Abstract

We solve an open problem concerning the existence of cycle-finite algebras of infinite representation type for which all indecomposable projective modules and indecomposable injective modules are nondirecting (lie on oriented cycles of indecomposable modules). We prove that there exist such algebras having large numbers of almost acyclic Auslander–Reiten components with finite cyclic multisections.

Authors

  • Piotr MalickiFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail
  • José Antonio de la PeñaCentro de Investigación en Matemáticas (CIMAT)
    Guanajuato, México
    e-mail
  • Andrzej SkowrońskiFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail

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