On tame repetitive algebras

Volume 142 / 1993

Ibrahim Assem, Andrzej Skowroński Fundamenta Mathematicae 142 (1993), 59-84 DOI: 10.4064/fm_1993_142_1_1_59_84


Let A be a finite dimensional algebra over an algebraically closed field, and denote by T(A) (respectively, Â) the trivial extension of A by its minimal injective cogenerator bimodule (respectively, the repetitive algebra of A). We characterise the algebras A such that  is tame and exhaustive, that is, the push-down functor mod  → mod T(A) associated with the covering functor  → T(A)\nsimto Â/(ν_A)$ is dense. We show that, if  is tame and exhaustive, then A is simply connected if and only if A is not an iterated tilted algebra of type $Â_m$. Then we prove that  is tame and exhaustive if and only if A is tilting-cotilting equivalent to an algebra which is either hereditary of Dynkin or Euclidean type or is tubular canonical.


  • Ibrahim AssemDépartement de Mathématiques
    et d’Informatique
    Université de Sherbrooke
    Sherbrooke, Québec
    Canada, J1K 2R1
  • Andrzej SkowrońskiInstitute of Mathematics
    Nicholas Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland

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