English

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.

Keywords

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

R2 v1 2026-06-22T11:46:57.722Z