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, equivalently the Drinfeld center of the category of representations of a finite group. Both operations are related to the $r$-th power operation, with $r$ relatively prime to the exponent of the group. One is defined more generally for the group-theoretical fusion category defined by a finite group and an arbitrary subgroup, while the other seems particular to the case of Yetter-Drinfeld modules. Both autoequivalences 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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Soumis le : mardi 25 avril 2017 - 17:36:37
Dernière modification le : vendredi 8 juin 2018 - 14:50:07

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Peter Schauenburg. Some quasitensor autoequivalences of Drinfeld doubles of finite groups. Journal of Noncommutative Geometry, European Mathematical Society, 2017, 11 (1), pp.51 - 70. ⟨10.4171/JNCG/11-1-2⟩. ⟨hal-01514158⟩



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