SOME QUASITENSOR AUTOEQUIVALENCES OF DRINFELD DOUBLES OF FINITE GROUPS

Peter Schauenburg (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Domaines: Algèbres quantiques [math.QA]; Anneaux et algèbres [math.RA]; Catégories et ensembles [math.CT]; Théorie des représentations [math.RT]

Peter Schauenburg. SOME QUASITENSOR AUTOEQUIVALENCES OF DRINFELD DOUBLES OF FINITE GROUPS. 2015. ⟨hal-01115406⟩