Adam-Christiaan Van Roosmalen (Bielefeld), Hereditary uniserial categories.

Abstract:

I will talk about a recent classification of hereditary uniserial categories with Serre duality. It is known, following work of Amdal and Ringdal, that there are two types of uniserial length categories: linear and cyclic. For hereditary Hom-finite categories, this dichotomy persists when one drops the length-condition but there are infinite examples of both types.

In the linear case, infinite examples have been constructed by Ringel; these examples come from an infinite version of an A_n quiver. In the cyclic case, we will construct an infinite version of a tube, called a big tube.

The talk will focus on describing the aforementioned infinite examples.