The group of braided autoequivalences of the category of comodules over a coquasi-triangular Hopf algebra
type: Item
instance of: scholarly article
title: The group of braided autoequivalences of the category of comodules over a coquasi-triangular Hopf algebra
zbMATH Open document ID: 1366.16027
author: Haixing Zhu
published in: Journal of Geometry and Physics
publication date: 2017-02-23T00:00:00Z
review text: Let \(H\) be a coquasi-triangular Hopf algebra and \(u_q(\mathrm{sl}(2))'\) the Lusztig's quantum group in the version of \textit{S. Gelaki} and \textit{S. Westreich} [J. Lond. Math. Soc., II. Ser. 57, No. 1, 105--125 (1998; Zbl 0933.16042)]. In the paper under review, the author uses the ordinary bi-Galois objects to investigate braided autoequivalences. Firstly, he shows that the group of braided autoequivalences of the category of \(H\)-comodules is isomorphic to the group of braided-commutative bi-Galois objects. As an application, he obtains that the group of braided auto-equivalences of the representation category of Lusztig's quantum group \(u_q(\mathrm{sl}(2))'\) is isomorphic to the projective special linear group \(\mathrm{PSL}(2)\), where \(q\) is a root of unity of odd order \(N>1\).
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 16K50
zbMATH DE Number: 6688394
zbMATH Keywords: coquasi-triangular Hopf algebra
zbMATH Keywords: Galois object
zbMATH Keywords: braided autoequivalence
reviewed by: Shilin Yang
MaRDI profile type: Publication
full work available at URL: j.geomphys.2016.10.021
OpenAlex ID: W2558722725
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DOI: 10.1016/J.GEOMPHYS.2016.10.021
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description: scientific article; zbMATH DE number 6688394