Bicommutant categories from fusion categories
Operator Algebras
2016-12-20 v2 Category Theory
Quantum Algebra
Abstract
Bicommutant categories are higher categorical analogs of von Neumann algebras that were recently introduced by the first author. In this article, we prove that every unitary fusion category gives an example of a bicommutant category. This theorem categorifies the well known result according to which a finite dimensional *-algebra that can be faithfully represented on a Hilbert space is in fact a von Neumann algebra.
Cite
@article{arxiv.1511.05226,
title = {Bicommutant categories from fusion categories},
author = {André Henriques and David Penneys},
journal= {arXiv preprint arXiv:1511.05226},
year = {2016}
}
Comments
Updated to the published version + fixed some small typos