Local Modules in Braided Fusion 2-categories
Organizers
Speaker
Hao Xu
Time
Wednesday, April 17, 2024 9:00 PM - 10:30 PM
Venue
Online
Online
Zoom 482 240 1589
(BIMSA)
Abstract
Given a braided algebra in a braided fusion 2-category, under certain rigidity condition, its modules form a monoidal 2-category. Refining the notion of module to local module, we prove that local modules over a separable braided algebra form a braided multifusion 2-category. Meanwhile, local modules and free modules centralise each other (generalising the 1-categorical setting), and satisfy a type of reciprocity (which is a new phenomenon emerging in the 2-categorical setting).
By analogy with Lagrangian algebras in braided 1-categories, we define a Lagrangian algebra in a braided fusion 2-category as a connected separable braided algebra whose local modules form a trivial 2-category $\mathbf{2Vect}$. Lagrangian algebras play an important role in classifying topological boundaries of (3+1)D topological orders. I will comment on how to address the parallel question in mathematics, that is the classification of (bosonic) fusion 2-categories, via Lagrangian algebras in the Drinfeld center of a strongly fusion 2-category $\mathbf{2Vect}^\pi_G$.
This talk is based on arXiv:2307.02843 (joint with Thibault Décoppet), arXiv:2403.07768 and an on-going project.
By analogy with Lagrangian algebras in braided 1-categories, we define a Lagrangian algebra in a braided fusion 2-category as a connected separable braided algebra whose local modules form a trivial 2-category $\mathbf{2Vect}$. Lagrangian algebras play an important role in classifying topological boundaries of (3+1)D topological orders. I will comment on how to address the parallel question in mathematics, that is the classification of (bosonic) fusion 2-categories, via Lagrangian algebras in the Drinfeld center of a strongly fusion 2-category $\mathbf{2Vect}^\pi_G$.
This talk is based on arXiv:2307.02843 (joint with Thibault Décoppet), arXiv:2403.07768 and an on-going project.