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Selecta Mathematica

, Volume 23, Issue 3, pp 1669–1708 | Cite as

Bicommutant categories from fusion categories

  • André Henriques
  • David Penneys
Article

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.

Notes

Acknowledgments

This project began at the 2015 Mathematisches Forschungsinstitut Oberwolfach workshop on Subfactors and conformal field theory. The authors would like to thank the organizers and MFO for their hospitality. André Henriques was supported by the Leverhulme trust and the EPSRC grant “Quantum Mathematics and Computation” during his stay in Oxford. David Penneys was partially supported by an AMS-Simons travel Grant and NSF DMS Grant 1500387.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Utrecht UniversityHans Freudenthal buildingUtrechtThe Netherlands
  2. 2.University of OxfordAndrew Wiles BuildingOxfordUK
  3. 3.The Oho State UniversityColumbusUSA

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