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

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

2001-08-20

arxiv.org/abs/math/0108131v2

Mathematics

Quantum Algebra

22 pages; the main result of Section 3 has been corrected in the revised version. The formula in Theorem 4.4 has also been aff

Scientific paper

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.

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