  The Hopf algebra generated by the l-functionals on the quantum double C_q[G]
\bowtie C_q[G] is considered, where C_q[G] is the coordinate algebra of a
standard quantum group and q is not a root of unity. It is shown to be
isomorphic to C_q[G]^op \bowtie U_q(g). This was conjectured by T. Hodges in
[Ho]. As an algebra it can be embedded into U_q(g) \otimes U_q(g). Here it is
proven that there is no bialgebra structure on U_q(g) \otimes U_q(g), for which
this embedding becomes a homomorphism of bialgebras. In particular, it is not
an isomorphism. As a preliminary a lemma of [Ho] concerning the structure of
l-functionals on C_q[G] 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.
