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Frobenius–Schur
indicators for near-group and Haagerup–Izumi fusion
categories
Henry Tucker |
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Vol. 303 (2019), No. 1, 337–359
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Abstract |
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Ng and Schauenburg generalized higher Frobenius–Schur indicators to pivotal fusion categories and showed that these indicators may be computed utilizing the modular data of the Drinfel’d center of the given category. We consider two classes of fusion categories generated by a single noninvertible simple object: near groups, those fusion categories with one noninvertible object, and Haagerup–Izumi categories, those with one noninvertible object for every invertible object. Examples of both types arise as representations of finite or quantum groups or as Jones standard invariants of finite-depth Murray–von Neumann subfactors. We utilize the computations of the tube algebras due to Izumi and to Evans and Gannon to obtain formulae for the Frobenius–Schur indicators of objects in both of these families. |
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Dedicated to Susan Montgomery |
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Keywords
tensor category, fusion rules, Frobenius–Schur indicator,
Drinfel'd center, modular data, Haagerup subfactor, Hopf
algebras
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Mathematical Subject Classification 2010
Primary: 18D10, 16T05
Secondary: 46L37
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Milestones
Received: 9 June 2017
Revised: 20 January 2019
Accepted: 29 January 2019
Published: 21 December 2019
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Authors |
| Henry Tucker | |
| Department of Mathematics University of California, San Diego La Jolla, CA United States |
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