The group of braided autoequivalences of the category of comodules over a coquasi-triangular Hopf algebra
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 \(N>1\).
scientific article; zbMATH DE number 6688394
scientific article