Geodesic
On tame repetitive algebras
Ibrahim Assem1 ; Andrzej Skowroński2
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
Fundamenta Mathematicae, Tome 142 (1993) no. 1, pp. 59-84.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm_1993_142_1_1_59_84

Ibrahim Assem 1 ; Andrzej Skowroński 2

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 
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Ibrahim Assem; Andrzej Skowroński. On tame repetitive algebras. Fundamenta Mathematicae, Tome 142 (1993) no. 1, pp. 59-84. doi : 10.4064/fm_1993_142_1_1_59_84. http://geodesic.mathdoc.fr/articles/10.4064/fm_1993_142_1_1_59_84/

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