Self-injective cores and (non-)cell 2-representations

  • Date: –17:00
  • Location: Zoom-möte
  • Lecturer: Mateusz Stroinski (Uppsala)
  • Organiser: Matematiska institutionen
  • Contact person: Volodymyr Mazorchuk
  • Seminarium

This is a presentation of a master's thesis.

In the study of 2-representations of finitary 2-categories, as introduced by Volodymyr Mazorchuk and Vanessa Miemietz, the notion of a simple transitive 2-representation is analogous to that of a simple module.

In an article published in 2019, Jakob Zimmermann studied such 2-representations of some 2-categories of projective bimodules over a certain associative algebra associated to n>0. Two cases were considered: in the first, simple transitive 2-representations were determined to be exhausted by cell 2-representations. In the second, it was conjectured that simple transitive 2-representations are in bijection with set partitions of the set {1,...,n}.

I will review the basics of representation theory for finitary 2-categories, introduce the notion of a self-injective core for an algebra, using which I will give a generalization of the aforementioned result of Zimmermann. For the second case of Zimmermann's article, I will describe a family of simple transitive 2-representations in bijection with said set partitions, which is a first step towards verifying the conjecture.