Emmy-Noether-Seminar: "Fusion quivers"
Gregor Schaumann (Würzburg)
Abstract: Quivers are combinatorial objects with many applications to representation theory, moduli spaces and (Hopf) algebras. From the point of view of quantum topology it is natural to study monoidal structures on the categories of modules over a given quiver.
In this talk we will first examine quivers from a categorical point of view, leading to an accessible description of their categories of modules in terms of linear categories. Then we discuss a quite general construction of rigid monoidal structures on the modules over a particular class of quivers, which generalizes in particular the Hopf quivers by Ciblis and Rosso. Finally we discuss a class of relations on these quivers which are adapted to the monoidal structures and find for example the Taft Hopf algebra via this construction.