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VOL. 80 | 2019 Reconstruction I. The classical part of a vertex operator algebra
Terry Gannon

Editor(s) Masaki Izumi, Yasuyuki Kawahigashi, Motoko Kotani, Hiroki Matui, Narutaka Ozawa

Abstract

It is known that the category of representations of a rational vertex operator algebra (RVOA) is a modular tensor category. An interesting and important question is the converse, reconstruction: given a modular tensor category $C$, is there a RVOA whose category of representations is $C$? In this paper we explain how, given $C$, to recover the affine algebra and lattice vertex operator subalgebras possible inside a RVOA realizing $C$. We apply this to the most celebrated 'exotic' modular tensor category: that associated to the Haagerup subfactor. Whether this can be done consistently is a highly nontrivial test of the existence of the still-hypothetical Haagerup VOA.

Information

Published: 1 January 2019
First available in Project Euclid: 21 August 2019

zbMATH: 07116423
MathSciNet: MR3966584

Digital Object Identifier: 10.2969/aspm/08010071

Subjects:
Primary: 17B69
Secondary: 18D10, 81T40

Rights: Copyright © 2019 Mathematical Society of Japan

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