Bicommutant categories from fusion categories

By A. Henriques, David Penneys. 2015

47 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/522564c6e72704d9378270d5efb21d549659c572

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In Algebra and Number Theory

1. David Penneys
2. Corey Jones

In Geometry and Topology

1. David Penneys
2. Corey Jones

In Mathematical Physics

1. David Penneys
2. Corey Jones

Citations in the corpus

• Operator Algebras in Rigid C*-Tensor Categories (2016, background): “and operator algebras. This has two important consequences. First, to dene an operator algebra internal to an involutive tensor category, we restrict our attention to bi-involutive tensor categories [HP15] which have a dagger structure compatible with the involutive structure. (In the graphical calc”