Ribbon categories crossed by crossed modules
演讲者
王邦鑫
时间
2026年06月08日 10:30 至 12:00
地点
A3-3-301
线上
Zoom 242 742 6089
(BIMSA)
摘要
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.