BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar Unitary braided tensor categories from operator algebras
Unitary braided tensor categories from operator algebras
Organizers
Linzhe Huang , Zhengwei Liu , Sebastien Palcoux , Yilong Wang , Jinsong Wu
Speaker
Quan Chen
Time
Wednesday, October 12, 2022 9:30 AM - 10:30 AM
Venue
1120
Online
Zoom 537 192 5549 (BIMSA)
Abstract
Given a W*-category C, we construct a unitary braided tensor category End_loc(C) of local endofunctors on C, which is a new construction of a braided tensor category associated with an arbitrary W*-category. For the W*-category of finitely generated projective modules over a von Neumann algebra M, this yields a unitary braiding on Popa's χ~(M), which extends Connes' χ(M) and Jone's kappa invariant. Given a finite depth inclusion M_0\subset M_1 of non-Gamma II_1 factors, we show that χ~(M_\infty) is equivalent to the Drinfeld center of the standard invariant, where M_infty is the inductive limit of the Jones tower of basic construction. This is joint work with Corey Jones and David Penneys (arXiv: 2111.06378).
Speaker Intro
Quan Chen is a postdoctoral researcher at Vanderbilt University, where he began his position in Fall 2023 under the mentorship of Professor Dietmar Bisch. He earned his Ph.D. in Mathematics from The Ohio State University in Spring 2023, working under the supervision of Professor David Penneys. His research interests lie in the areas of operator algebras, subfactor theory, and quantum algebra.