The group of braided autoequivalences of the category of comodules over a coquasi-triangular Hopf algebra

Let H be a coquasi-triangular Hopf algebra. We first show that the group of braided autoequivalences of the category of H-comodules is isomorphic to the group of braided-commutative bi-Galois objects. Next, by investigating the latter, we obtain that the group of braided autoequivalences of the representation category of Lusztig's quantum group uq(sl(2))′ is isomorphic to the projective special linear group PSL(2), where q is a root of unity of odd order N>1.