BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar Constructing modular tensor categories by using Hopf algebras
Constructing modular tensor categories by using Hopf algebras
Organizers
Lin Zhe Huang , Zheng Wei Liu , Sebastien Palcoux , Yi Long Wang , Jin Song Wu
Speaker
Kun Zhou
Time
Wednesday, April 10, 2024 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
A modular tensor category is a non-degenerate ribbon finite tensor category. We will construct ribbon factorizable Hopfalgebras whose representation categories are modular tensor categories. Specifically, we give some general constructionmethods of ribbon factorizable Honf algebras. Then we use these methods to obtain a family of semisimple ribborfactorizable Hopf algebras and two families of non-semisimple ribbon factorizable Hopf algebras. The representationcategories of the last two families are prime modular tensor categories, while the representation categories of first family arenot prime modular tensor categories. Finally, we compared their representation categories with known modular tensorcategories from ribbon factorizable Hopf algebras in some degree.