Braided autoequivalences, quantum commutative Galois objects and the Brauer groups | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Braided autoequivalences, quantum commutative Galois objects and the Brauer groups

De Yinhuo Zhang

Apparaît dans les collections : Algebra, deformations and quantum groups / Algèbre, déformations et groupes quantiques, Exposés de recherche

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.

Informations sur la vidéo

Date de captation 04/12/2014
Date de publication 11/12/2014
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.18650203
Citer cette vidéo Zhang, Yinhuo (04/12/2014). Braided autoequivalences, quantum commutative Galois objects and the Brauer groups. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18650203
URL https://dx.doi.org/10.24350/CIRM.V.18650203

Domaine(s)

Algèbres quantiques

Bibliographie

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
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

Codes MSC

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2025

Donner son avis