BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar On perfect modualr categories of low dimension
On perfect modualr categories of low dimension
Organizers
Lin Zhe Huang , Zheng Wei Liu , Sebastien Palcoux , Yi Long Wang , Jin Song Wu
Speaker
JingCheng Dong
Time
Wednesday, November 20, 2024 2:00 PM - 3:15 PM
Venue
A3-3-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
In this talk, we prove that modular categories of Frobenius-Perron dimension $p^2q^2r^2m$ are solvable, where $p,q,r$ are distinct prime numbers, $m$ is square-free with $gcd(m,pqr)=1$. As applications, we get that integral modular categories of Frobenius-Perron dimension less than 1800 are solvable, and hence integral perfect modular categories have Frobenius-Perron dimension greater than or equal to 1800. When the modular categories considered are weakly group-theoretical, we get some further results.