Algebra and Combinatorics Seminar

Date: November 10, 2017

Time: 3:00PM - 3:50PM

Location: BLOC 117

Speaker: Henry Tucker, UC San Diego

Title: Invariants and realizations of near-group fusion categories

Abstract: Classification of fusion categories by possible ring structures realized by the tensor product was first considered by Eilenberg-Mac Lane in the case where all objects are invertible under the tensor product, i.e. the Grothendieck ring is a group ring. More recently Tambara-Yamagami, Izumi, Evans-Gannon, and others have established classification results for near-group fusion categories: those with a Grothendieck ring with basis a monoid consisting of a group adjoined with a single non-invertible element. In this talk we will survey the classification results on these categories with an emphasis on the dichotomy between the cases determined by the integrality of the non-invertible object. Specifically, in the integral case it is known that the categories are group-theoretical, and in this case we will discuss quasi-Hopf algebra realizations given by cleft extensions.