On tame repetitive algebras
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 Â is tame and exhaustive, that is, the push-down functor mod Â → mod T(A) associated with the covering functor Â → T(A)\nsimto Â/(ν_A)$ is dense. We show that, if Â 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 Â 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.