1-step beyond semisimple algebras: fusion quivers

Abstract: The study of module categories over fusion categories have focussed mostly on the semisimple ones. In this talk I will introduce the notion of fusion quivers and their representations, the categories of which form hereditary (global projective dimension 1) abelian module categories over fusion categories. This naive “one-step” generalisation from semisimple module categories uncovers a wealth of interesting new connections to Coxeter theory. In particular, I will present a classification result in the spirit of Gabriel: the finite-representation-type fusion quivers are classified by the Coxeter—Dynkin diagrams; the latter includes the (crystallographic) Dynkin diagram from Lie algebras ABCDEFG and, perhaps surprisingly, also the non-crystallographic diagrams H and I, which all together classify the finite Coxeter groups. This is based on joint work with Ben Elias.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home