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VOL. 46 | 2017 Free Analysis and Planar Algebras
S. Curran, Y. Dabrowski, D. Shlyakhtenko

Editor(s) Scott Morrison, David Penneys

Proc. Centre Math. Appl., 2017: 115-142 (2017)


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-$\Gamma$ non-$L^2$ rigid factors.


Published: 1 January 2017
First available in Project Euclid: 21 February 2017

zbMATH: 06990152
MathSciNet: MR3635669

Rights: Copyright © 2017, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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