Liftings of graded quasi-Hopf algebras with radical of prime codimension

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dc.creatorEtingof, Pavel
dc.creatorGelaki, Shlomo
dc.date2004-12-07
dc.date.accessioned2026-07-07T05:15:03Z
dc.date.available2026-07-07T05:15:03Z
dc.descriptionLet p be a prime, and let RG(p) denote the set of equivalence classes of radically graded finite dimensional quasi-Hopf algebras over C, whose radical has codimension p. The purpose of this paper is to classify finite dimensional quasi-Hopf algebras A whose radical is a quasi-Hopf ideal and has codimension p; that is, A with grA in RG(p), where grA is the associated graded algebra taken with respect to the radical filtration on A. The main result of this paper is the following theorem: Let A be a finite dimensional quasi-Hopf algebra whose radical is a quasi-Hopf ideal of prime codimension p. Then either A is twist equivalent to a Hopf algebra, or it is twist equivalent to H(2), H_\pm(p), A(q), or H(32), constructed in math.QA/0310253, math.QA/0402159 and math.QA/0403096. Note that any finite tensor category whose simple objects are invertible and form a group of order p under tensor is the representation category of a quasi-Hopf algebra A as above. Thus this paper provides a classification of such categories.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0412143
dc.identifierhttp://arxiv.org/abs/math/0412143
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73510
dc.subjectQuantum Algebra
dc.subject16W30
dc.titleLiftings of graded quasi-Hopf algebras with radical of prime codimension
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