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

Abstract

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 u q ( s l ( 2 ) ) ′ is isomorphic to the projective special linear group P S L ( 2 ) , where q is a root of unity of odd order N > 1 .