Noncommutative Geometry Seminar - Cain Edie-Michell

November 6, 2018
Thursday, November 8, 2018 - 1:50pm to 2:45pm
Math Building 105
Noncommutative Geometry Seminar

Title: Classifying fusion categories generated by an object of small dimension.

Speaker: Cain Edie-Michell (Vanderbilt University)

Abstract: One of the main goals in the study of fusion categories is to provide a complete classification result. However at the current time not even a conjectural description of all fusion categories has been given. Because a complete classification is completely out of reach with current techniques, current research on fusion categories focuses on classifying ``small” fusion categories, where small can have a variety of different meanings. For this talk, small will mean generated by an object of small Frobenius-Perron dimension. I will discuss a recent partial classification result of mine along these lines. I assume the generating object has dimension less than 2, along with a mild assumption on the commutativity of the generating object. This classification contains some very surprising categories, including some exceptional quantum subgroups.

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