1-step away from semisimple algebras in fusion categories and beyond
组织者
演讲者
Edmund Heng
时间
2025年07月10日 13:30 至 14:30
地点
A3-4-101
摘要
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. If time allows, I will discuss my grand goal of developing a foundational theory of all algebras in fusion categories, akin to the theory of finite dimensional algebras. This is based on joint work with Ben Elias and ongoing work with Mateusz Stroinski.