Liftings of graded quasi-Hopf algebras with radical of prime codimension |
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Authors: | Pavel Etingof |
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Institution: | a Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA b Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel |
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Abstract: | Let 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 gr(A) in RG(p), where gr(A) 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±(p), A(q), or H(32), constructed in 5] and 8]. 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. |
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Keywords: | 16W30 |
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