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BIMSA-Tsinghua Quantum Symmetry Seminar
BIMSA-Tsinghua Quantum Symmetry Seminar
Ribbon categories crossed by crossed modules
Ribbon categories crossed by crossed modules
Organizers
Speaker
Bangxin Wang
Time
Monday, June 8, 2026 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
We begin by recalling the notion of a G-crossed ribbon category. We then explain how to generalise this notion to a setting in which the grading group
and the acting group are different. It turns out that, in order to formulate a crossed braiding in this setting, the grading group and the acting group should form a crossed module. This leads us to introduce the notion of a $\chi$-crossed ribbon category associated with a crossed module $\chi$. We will discuss a construction of such categories via twisted local modules in a braided tensor category, and present classification results in the case of pointed fusion categories. This is joint work with Azat Gainutdinov and Ingo Runkel.
and the acting group are different. It turns out that, in order to formulate a crossed braiding in this setting, the grading group and the acting group should form a crossed module. This leads us to introduce the notion of a $\chi$-crossed ribbon category associated with a crossed module $\chi$. We will discuss a construction of such categories via twisted local modules in a braided tensor category, and present classification results in the case of pointed fusion categories. This is joint work with Azat Gainutdinov and Ingo Runkel.