BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar The computation on the Brauer group of a quasitriangular Hopf algebra
The computation on the Brauer group of a quasitriangular Hopf algebra
Organizers
Lin Zhe Huang , Zheng Wei Liu , Sebastien Palcoux , Yi Long Wang , Jin Song Wu
Speaker
Haixing Zhu
Time
Wednesday, December 11, 2024 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
Let (H, R) be a Hopf algebra H with the quasitriangular structure R (i.e., R-matrix). The Brauer group Br(H, R) of a quasitriangular Hopf algebra is the group of the equivalence classes of H-Azumaya algebras. It is also described as specific braided autoequivalences on the Drinfeld center of the category of H-modules. We will first describe the Drinfeld center of the representation category as the category of comodules over the braided Hopf algebra HR, which is deformed by R-matrix. This description helps us realize specific autoequivalences on the Drinfeld center by some quantum-commutative Galois objects. Then the group of these Galois objects is naturally related to the Brauer group Br(H, R), and actually appeared in an exact sequence of the Brauer group Br(H, R), which was constructed by Prof. Yinhuo Zhang. Next we will investigate how to construct / characterize these Galois objects, and mainly use Sweedler’s cohomology of the braided Hopf algebra HR to give its subgroup, and then get some information on Br(H, R).