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H 1 Braided autoequivalences, quantum commutative Galois objects and the Brauer groups

Auteurs : Zhang, Yinhuo (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Let $(H, R)$ be a finite dimensional quasitriangular Hopf algebra over a field $k$, and $_H\mathcal{M}$ the representation category of $H$. In this paper, we study the braided autoequivalences of the Drinfeld center $_H^H\mathcal{Y}\mathcal{D}$ trivializable on $_H\mathcal{M}$. We establish a group isomorphism between the group of those autoequivalences and the group of quantum commutative bi-Galois objects of the transmutation braided Hopf algebra $_RH$. We then apply this isomorphism to obtain a categorical interpretation of the exact sequence of the equivariant Brauer group $BM(k, H, R)$ established by Zhang. To this end, we have to develop the braided bi-Galois theory initiated by Schauenburg, which generalizes the Hopf bi-Galois theory over usual Hopf algebras to the one over braided Hopf algebras in a braided monoidal category.

    Codes MSC :
    16K50 - Brauer groups [See also 12G05, 14F22]
    16T05 - Hopf algebras and their applications

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 11/12/14
      Date de captation : 04/12/14
      Collection : Research talks ; Algebra
      Format : quicktime ; audio/x-aac
      Durée : 00:38:44
      Domaine : Algebra
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-12-04_Zhang.mp4

    Informations sur la rencontre

    Nom de la rencontre : Algebra, deformations and quantum groups / Algèbre, déformations et groupes quantiques
    Organisateurs de la rencontre : Kulish, Peter ; Makhlouf, Abdenacer ; Paal, Eugen ; Schlichenmaier, Martin ; Stolin, Alexander
    Dates : 01/12/14 - 05/12/14
    Année de la rencontre : 2014

    Citation Data

    DOI : 10.24350/CIRM.V.18650203
    Cite this video as: Zhang, Yinhuo (2014). Braided autoequivalences, quantum commutative Galois objects and the Brauer groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18650203
    URI : http://dx.doi.org/10.24350/CIRM.V.18650203


    1. Zhang, Y., & Zhu, H. (2013) Braided autoequivalences and quantum commutative bi-Galois objects. Preprint, arXiv:1312.3800v1 [math.QA] - http://arxiv.org/abs/1312.3800

    2. Dello, J., & Zhang, Y. (2014) Braided autoequivalences and the equivariant Brauer group of a quasitriangular Hopf algebra. Preprint, arXiv:1410.8686v1 [math.QA] - http://arxiv.org/abs/1410.8686

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