FRT-duals as quantum enveloping algebras

AbstractThe Hopf algebra generated by the l-functionals on the quantum double Cq[G]⋈Cq[G] is considered, where Cq[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 Cq[G]op⋈Uq(g). This proves a conjecture by T. Hodges. As an algebra it can be embedded into Uq(g)⊗Uq(g). Here it is proven that there is no bialgebra structure on Uq(g)⊗Uq(g), 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 Cq[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