Helene Tyler, Manhattan College
Classification of Module Categories via the Gabriel-Roiter Measure
This talk reflects joint work with Markus Schmidmeier

The Gabriel-Roiter measure of a module was introduced in 2005 by C.M. Ringel. It is based on P. Gabriel's refinement of the induction scheme that A. Roiter used in his proof of the first Brauer-Thrall conjecture. The Gabriel-Roiter measure provides a tripartite classification mechanism for the category of modules over a finite-dimensional algebra, alternative to the traditional classification offered by the Auslander-Reiten theory. In earlier work, we undertook a detailed study of the Gabriel-Roiter measures for tame hereditary quivers of type $\widetilde{\mathbb A}_n$, and their interplay with the Auslander-Reiten theory. In our current work, we expand our purview to a larger class of algebras for which the Auslander-Reiten theory is well understood, but the effect on the Gabriel-Roiter theory was not yet known.