Classification of finite depth objects in bicommutant categories via anchored planar algebras

Journal article

Abstract:: In our article [arXiv:1511.05226], we studied the commutant C′ ⊂ Bim(R) of a unitary fusion category C, where R is a hyperfinite factor of type II1, II∞, or III1, and showed that it is a bicommutant category. In other recent work [arXiv:1607.06041, arXiv:2301.11114] we introduced the notion of a (unitary) anchored planar algebra in a (unitary) braided pivotal category D, and showed that they classify (unitary) module tensor categories for D equipped with a distinguished object. Here, we connect these two notions and show that finite depth objects of C′ are classified by connected finite depth unitary anchored planar algebras in Z(C). This extends the classification of finite depth objects of Bim(R) by connected finite depth unitary planar algebras.

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Copyright holder:: Henriques et al.
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