# Mathematical Sciences Research Institute

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# Seminar

QS - Seminar: A classification of fusion categories generated by a small normal object March 12, 2020 (02:00 PM PDT - 03:00 PM PDT)
Parent Program: Quantum Symmetries MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Cain Edie-Michell (Vanderbilt University)
Description No Description
Video

#### 3-Edie-Michell

Abstract/Media

This talk will be livestreamed.  Join here: https://msri.zoom.us/j/627176824

The Jones index theorem gives strong restrictions on the dimensions of small objects in fusion categories. In particular it implies that if $\dim(X) <2$, then $\dim(X)$ must lie in the discrete set $\{ 2\cos(\frac{pi}{n}\}$. Further, the theorem gives a concrete example for each n. However the converse problem of classifying all objects of dimension less than 2 is still open. In this talk we will give a partial answer to this converse problem. With the additional mild assumption that $X \otimes X^* \cong X^* \otimes X$ we will give a full classification of fusion categories generated by an object of dimension less than 2. Our classification includes the expected examples, such as cyclic groups and the ADET categories, but also includes several surprising examples coming from quantum subgroups of low rank Lie algebras.