Generalized cones as Lorentzian length spaces: Causality, curvature, and
singularity theorems
Alexander, S Graf, M Kunzinger, M Sämann, C (20 Sep 2019) http://arxiv.org/abs/1909.09575v2
Nonlinear electrochemical impedance spectroscopy for lithium-ion battery model parameterization
Kirk, T Lewis-Douglas, A Howey, D Please, C Chapman, S Journal of The Electrochemical Society volume 170 issue 1 (13 Jan 2023)
Tue, 24 Jan 2023
16:00
C3

Braided tensor categories as invariants of von Neumann algebras

Corey Jones
(North Carolina State University)
Abstract

In the operator algebraic approach to quantum field theory, the DHR category is a braided tensor category describing topological point defects of a theory with at least 1 (+1) dimensions. A single von Neumann algebra with no extra structure can be thought of as a 0 (+1) dimensional quantum field theory. In this case, we would not expect a braided tensor category of point defects since there are not enough dimensions to implement a braiding. We show, however, that one can think of central sequence algebras as operators localized ``at infinity", and apply the DHR recipe to obtain a braided tensor category of bimodules of a von Neumann algebra M, which is a Morita invariant. When M is a II_1 factor, the braided subcategory of automorphic objects recovers Connes' chi(M) and Jones' kappa(M). We compute this for II_1 factors arising naturally from subfactor theory and show that any Drinfeld center of a fusion category can be realized. Based on joint work with Quan Chen and Dave Penneys.

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