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Computing the Frobenius–Schur Indicator for Abelian Extensions of Hopf Algebras
- Source :
- Journal of Algebra. 251(2):888-913
- Publication Year :
- 2002
- Publisher :
- Elsevier BV, 2002.
-
Abstract
- 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.
- Subjects :
- Discrete mathematics
Pure mathematics
Algebra and Number Theory
Quantum group
010102 general mathematics
Elementary abelian group
Representation theory of Hopf algebras
Schur algebra
Quasitriangular Hopf algebra
Hopf algebra
01 natural sciences
Frobenius–Schur indicator
Mathematics::Quantum Algebra
0103 physical sciences
010307 mathematical physics
0101 mathematics
Abelian group
Mathematics
Subjects
Details
- ISSN :
- 00218693
- Volume :
- 251
- Issue :
- 2
- Database :
- OpenAIRE
- Journal :
- Journal of Algebra
- Accession number :
- edsair.doi.dedup.....52dc43d02dce3eb8f238e223c00c9f82
- Full Text :
- https://doi.org/10.1006/jabr.2001.9129