Computing the Frobenius–Schur Indicator for Abelian Extensions of Hopf Algebras☆☆☆
By Yevgenia Kashina, Geoffrey Mason, S. Montgomery. 2001
63 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6f660f4804c1b86088285efe0e634fd2865a0b83
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In Algebra and Number Theory
- Siu-Hung Ng
- Geoffrey Mason
- Yevgenia Kashina
- Yorck Sommerhaeuser
- Yongchang Zhu
- Peter Schauenburg
- Michael Mueger
- Christopher D. Goff
In Geometry and Topology
- Siu-Hung Ng
- Geoffrey Mason
- Yevgenia Kashina
- Yorck Sommerhaeuser
- Yongchang Zhu
- Peter Schauenburg
- Michael Mueger
- F. Pellarin
In Mathematical Physics
Citations in the corpus
- On higher Frobenius-Schur indicators (2003, background): “For this, we need a description of the irreducible modules and their characters, which we take from [22], Sec.”
- Central invariants and Frobenius–Schur indicators for semisimple quasi-Hopf algebras (2003, methodology): “4 of [16] can be used to obtain indicators ARTICLE IN PRESS”