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N°Spécial De Revue/Special Issue Proceedings of the Centre for Mathematics and its Applications Année : 2017

Free Analysis and Planar Algebras

Stephen Curran
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Résumé

We study 2-cabled analogs of Voiculescu’s trace and free Gibbs states on Jones planar algebras. These states are traces on a tower of graded algebras associated to a Jones planar algebra. Among our results is that, with a suitable definition, finiteness of free Fisher information for planar algebra traces implies that the associated tower of von Neumann algebras consists of factors, and that the standard invariant of the associated inclusion is exactly the original planar algebra. We also give conditions that imply that the associated von Neumann algebras are non-Γ non-L2 rigid factors.
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Dates et versions

hal-02069995 , version 1 (16-03-2019)

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  • HAL Id : hal-02069995 , version 1

Citer

Yoann Dabrowski, Dimitri Shlyakhtenko, Stephen Curran. Free Analysis and Planar Algebras. Scott Morrison and David Penneys, eds. Proceedings of the Centre for Mathematics and its Applications, 46, pp.115 - 142, 2017, Proc. of the 2014 Maui and 2015 Qinhuangdao Conf. in Honour of Vaughan F.R. Jones’ 60th Birthday. ⟨hal-02069995⟩
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