From finite to infinite length modules over tame hereditary algebras

Abstract

A self-contained introduction to infinite dimensional representations over a tame hereditary algebra is provided, assuming a basic knowledge of the category of finite dimensional representations. This includes a complete description of all pure-injective modules. Of particular interest are the torsionfree divisible modules, which are precisely the direct sums of copies of the unique generic module.

24 pages. Submitted for publication in "Annals of Representation Theory" (special volume on the occasion of Claus Michael Ringel's 80th birthday). New version contains an appendix which clarifies/unifies some of the arguments used thoughout the main part