Computing the Frobenius-Schur indicator for abelian extensions of Hopf algebras

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In this paper we show that for an important class of non-trivial Hopf algebras, the Schur indicator is a computable invariant. The Hopf algebras we consider are all abelian extensions; as a special case, they include the Drinfeld double of a group algebra. In addition to finding a general formula for the indicator, we also study when it is always positive. In particular we prove that the indicator is always positive for the Drinfeld double of the symmetric group, generalizing the classical result for the symmetric group itself.
22 pages; the main result of Section 3 has been corrected in the revised version. The formula in Theorem 4.4 has also been affected by this correction

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Quantum Algebra, Rings and Algebras, Representation Theory, 16W30

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http://salesiana.dossiersoluciones.com/handle/123456789/62045

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108131
 http://arxiv.org/abs/math/0108131

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arXiv