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Unitary Anchored Planar Algebras

https://doi.org/10.1007/s00220-024-04985-w

Henriques, André; Penneys, David; Tener, James (May 2024, Communications in Mathematical Physics)

Abstract In our previous article (http://arxiv.org/abs/1607.06041), we established an equivalence between pointed pivotal module tensor categories and anchored planar algebras. This article introduces the notion of unitarity for both module tensor categories and anchored planar algebras, and establishes the unitary analog of the above equivalence. Our constructions use Baez’s 2-Hilbert spaces (i.e., semisimple$$\textrm{C}^*$$ $C^{*}$ -categories equipped with unitary traces), the unitary Yoneda embedding, and the notion of unitary adjunction for dagger functors between 2-Hilbert spaces.
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The Classification of Subfactors with Index at Most 5\frac{1}4

https://doi.org/10.1090/memo/1405

Afzaly, Narjess; Morrison, Scott; Penneys, David (April 2023, Memoirs of the American Mathematical Society)

Subfactor standard invariants encode quantum symmetries. The small index subfactor classification program has been a rich source of interesting quantum symmetries. We give the complete classification of subfactor standard invariants to index $5 \frac{1}{4}$ , which includes $3 + \sqrt{5}$ , the first interesting composite index.
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Operator Algebras in Rigid C*-Tensor Categories

https://doi.org/10.1007/s00220-017-2964-0

Jones, Corey; Penneys, David (November 2017, Communications in Mathematical Physics)

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