The representation category of the quantum group of a non-degenerate bilinear form

Abstract

We show that the representation category of the quantum group of a non-degenerate bilinear form is monoidally equivalent to the representation category of the quantum group SL_q(2), for a well chosen non-zero parameter q. The main ingredient for the proof of this result is the direct and explicit construction of an appropriate Hopf bigalois extension. Then we get, in characteristic zero, a full description of cosemisimple Hopf algebras whose representation semi-ring is isomorphic to the one of SL(2).