Group-theoretical properties of nilpotent modular categories

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dc.creatorDrinfeld, Vladimir
dc.creatorGelaki, Shlomo
dc.creatorNikshych, Dmitri
dc.creatorOstrik, Victor
dc.date2007-04-02
dc.date2007-04-02
dc.date.accessioned2026-07-07T07:54:23Z
dc.date.available2026-07-07T07:54:23Z
dc.descriptionWe characterize a natural class of modular categories of prime power Frobenius-Perron dimension as representation categories of twisted doubles of finite p-groups. We also show that a nilpotent braided fusion category C admits an analogue of the Sylow decomposition. If the simple objects of C have integral Frobenius-Perron dimensions then C is group-theoretical. As a consequence, we obtain that semisimple quasi-Hopf algebras of prime power dimension are group-theoretical. Our arguments are based on a reconstruction of twisted group doubles from Lagrangian subcategories of modular categories (this is reminiscent to the characterization of doubles of quasi-Lie bialgebras in terms of Manin pairs).
dc.description23 pages, LaTeX, typos corrected
dc.identifierhttps://arxiv.org/abs/0704.0195
dc.identifierhttp://arxiv.org/abs/0704.0195
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126587
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.titleGroup-theoretical properties of nilpotent modular categories
dc.typetext

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