SOME QUASITENSOR AUTOEQUIVALENCES OF DRINFELD DOUBLES OF FINITE GROUPS

Abstract : We report on two classes of autoequivalences of the category of Yetter-Drinfeld modules over a finite group, or, equiv-alently the Drinfeld center of the category of representations of a finite group. Both operations are related to the r-th power opera-tion, with r relatively prime to the exponent of the group. One is defined more generally for the group-theoretical fusion category de-fined by a finite group and an arbitrary subgroup, while the other seems particular to the case of Yetter-Drinfeld modules. Both au-toequivalences preserve higher Frobenius-Schur indicators up to Galois conjugation, and they preserve tensor products, although neither of them can in general be endowed with the structure of a monoidal functor.
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https://hal.archives-ouvertes.fr/hal-01115406
Contributeur : Peter Schauenburg <>
Soumis le : mercredi 11 février 2015 - 10:35:32
Dernière modification le : mardi 12 janvier 2016 - 12:58:01
Document(s) archivé(s) le : samedi 12 septembre 2015 - 10:52:07

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1502.02902v1.pdf
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  • HAL Id : hal-01115406, version 1
  • ARXIV : 1502.02902

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Peter Schauenburg. SOME QUASITENSOR AUTOEQUIVALENCES OF DRINFELD DOUBLES OF FINITE GROUPS. 2015. <hal-01115406>

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