BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar Unitary braided tensor categories from operator algebras
Unitary braided tensor categories from operator algebras
Organizers
Lin Zhe Huang , Zheng Wei Liu , Sébastien Palcoux , Yi Long Wang , Jin Song 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
I am a six-year graduate student in the Department of Mathematics at the Ohio State University, working under the supervision of Prof. David Penneys. I am interested in operator algebra, especially subfactor theory and C*-algebras, (unitary/braided) tensor category, and low dimensional higher category theory.