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ArticleOriginal scientific text

Title

On tame repetitive algebras

Authors 1, 2

Affiliations

  1. Département de Mathématiques et d'Informatique, Université de Sherbrooke, Sherbrooke, Québec, Canada, J1K 2R1
  2. Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

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)isdense.Weshowt,^ifÂistameandexhaustive,thenAis∼plyco∩ectedifandonlyifAis¬aniteratedti<edal≥braoftypeÂ_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.

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Fundamenta Mathematicae
1993/142/1
Export to PBN, Opens in new tab
Pages:
59-84
Main language of publication
English
Received
1991-09-30
Accepted
1992-06-03
Published
1993
Exact and natural sciences