MATHEMATICAE

On tame repetitive algebras by Ibrahim As s em (Sherbrooke, Qué.) and Andrzej Sk owr o n ́ s k i (Toruń) Abstract. Let A be a finite dimensional algebra over an algebraically closed field, and denote by T (A) (respectively, A ̂ ) the trivial extension of A by its minimal injective cogenerator bimodule (respectively, the repetitive algebra of A). We characterise the algebras A such that A ̂ is tame and exhaustive, that is, the push-down functor mod A ̂ → modT (A) associated with the covering functor A ̂ → T (A)→ ∼ A ̂ /(νA) is dense. We show that, if A ̂ is tame and exhaustive, then A is simply connected if and only if A is not an iterated tilted algebra of type Ãm. Then we prove that A ̂ 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. Introduction. Let k denote an algebraically closed field, and A be a finite dimensional k-algebra (associative, with an identity) which we shal