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VOL. 46 | 2017 A Cuntz algebra approach to the classification of near-group categories


We classify $C^\ast$ near-group categories by using Vaughan Jones theory of subfactors and the Cuntz algebra endomorphisms. Our results show that there is a sharp contrast between two essentially different cases, integral and irrational cases. When the dimension of the unique non-invertible object is an integer, we obtain a complete classification list, and it turns out that such categories are always group theoretical. When it is irrational, we obtain explicit polynomial equations whose solutions completely classify the $C^\ast$ near-group categories in this class.


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

zbMATH: 06990156
MathSciNet: MR3635673

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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