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
Contributor : Peter Schauenburg <>
Submitted on : Wednesday, February 11, 2015 - 10:35:32 AM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
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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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