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On a necessary condition for unitary categorification of fusion rings

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arxiv 2102.13239 v2 pith:52HEIJOA submitted 2021-02-26 math.QA

Pavel Etingof , Dmitri Nikshych , Victor Ostrik This is my paper · ORCID
classification math.QA
keywords fusioncategorificationconditioninvariantsnecessaryringunitaryadmit
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In arXiv:1910.12059 Liu, Palcoux and Wu proved a remarkable necessary condition for a fusion ring to admit a unitary categorification, by constructing invariants of the fusion ring that have to be positive if it is unitarily categorifiable. The main goal of this note is to provide a somewhat more direct proof of this result. In the last subsection we discuss integrality properties of the Liu-Palcoux-Wu invariants.

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  1. Alterfold Theory and Topological Modular Invariance

    math.QA 2024-12 conditional novelty 6.0 of 10

    Alterfold TQFT gives a unified topological proof framework for modular invariants, alpha-induction, and flat connections, plus new higher-genus and multi-context invariants.

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