FRT-duals as quantum enveloping algebras

The Hopf algebra generated by the l-functionals on the quantum double is considered, where is the coordinate algebra of a standard quantum group and q is not a root of unity. It is shown to be isomorphic to . This proves a conjecture by T. Hodges. As an algebra it can be embedded into . Here it is proven that there is no bialgebra structure on , for which this embedding becomes a homomorphism of bialgebras. In particular, it is not an isomorphism. As a preliminary a lemma of Hodges concerning the structure of l-functionals on is generalized. For the classical groups a certain choice of root vectors is expressed in terms of l-functionals. A formula for their coproduct is derived.