Bicommutant categories from fusion categories

• André Henriques ^[1] ; David Penneys ^[2]
  1. [1] Utrecht University

     Utrecht University

     Países Bajos

     
  2. [2] The Oho State University
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 3, 2017, págs. 1669-1708
• Idioma: inglés
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• Resumen

  • 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.