Central Invariants and Higher Indicators for Semisimple Quasi-Hopf Algebras

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dc.creatorNg, Siu-Hung
dc.creatorSchauenburg, Peter
dc.date2005-08-08
dc.date2005-12-31
dc.date.accessioned2026-07-07T08:51:21Z
dc.date.available2026-07-07T08:51:21Z
dc.descriptionIn this paper, we define the higher Frobenius-Schur (FS-)indicators for finite-dimensional modules $V$ of a semisimple quasi-Hopf algebra $H$ via the categorical counterpart developed in \cite{NS05}. We prove that this definition of higher FS-indicators coincides with the higher indicators introduced by Kashina, Sommerhäuser, and Zhu when $H$ is a Hopf algebra. We also obtain a sequence of canonical central elements of $H$, which is invariant under gauge transformations, whose values, when evaluated by the character of an $H$-module $V$, are the higher Frobenius-Schur indicators of $V$. As an application, we show that FS-indicators are sufficient to distinguish the four gauge equivalence classes of semisimple quasi-Hopf algebras of dimension eight corresponding to the four fusion categories with certain fusion rules classified by Tambara and Yamagami. Three of these categories correspond to well-known Hopf algebras, and we explicitly construct a quasi-Hopf algebra corresponding to the fourth. We also derive explicit formulae for FS-indicators for some quasi-Hopf algebras associated to group cocycles.
dc.descriptionThe higher Frobenius-Schur indicators for certain quasi-Hopf algebras associated with finite groups and their 3-cocycles have been computed in section 7
dc.identifierhttps://arxiv.org/abs/math/0508140
dc.identifierhttp://arxiv.org/abs/math/0508140
dc.identifierTrans. Amer. Math. Soc. 360 (2008), 1839-1860 (Final Version)
dc.identifierdoi:10.1090/S0002-9947-07-04276-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144908
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.titleCentral Invariants and Higher Indicators for Semisimple Quasi-Hopf Algebras
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