Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9518188 | Advances in Mathematics | 2005 | 35 Pages |
Abstract
In this paper, we obtain a canonical central element νH for each semi-simple quasi-Hopf algebra H over any field k and prove that νH is invariant under gauge transformations. We show that if k is algebraically closed of characteristic zero then for any irreducible representation of H which affords the character Ï,Ï(νH) takes only the values 0, 1 or â1, moreover if H is a Hopf algebra or a twisted quantum double of a finite group then Ï(νH) is the corresponding Frobenius-Schur indicator. We also prove an analog of a theorem of Larson-Radford for split semi-simple quasi-Hopf algebras over any field k. Using this result, we establish the relationship between the antipode S, the values of Ï(νH), and certain associated bilinear forms when the underlying field k is algebraically closed of characteristic zero.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Geoffrey Mason, Siu-Hung Ng,