北京雁栖湖应用数学研究院

黄林哲 , 刘正伟 , Sébastien Palcoux , 王亦龙 , 吴劲松

陈权

2022年10月12日 09:30 至 10:30

1120

Zoom 537 192 5549 (BIMSA)

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).

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.