The Representation Category of the Quantum Group of a Non-degenerate Bilinear Form

Abstract

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 key ingredient for the proof of this result is the direct and explicit construction of an appropriate Hopf bigalois extension. Then we get, when the base field is of characteristic zero, a full description of cosemisimple Hopf algebras whose representation semi-ring is isomorphic to the one of SL(2).