The FRT-construction via quantum affine algebras and smash products

For every element w in the Weyl group of a simple Lie algebra g, De Concini, Kac, and Procesi defined a subalgebra of the quantized universal enveloping algebra Uq(g). The algebra is a deformation of the universal enveloping algebra U(n+∩w.n−). We construct smash products of certain finite-type De Concini–Kac–Procesi algebras to obtain ones of affine type; we have analogous constructions in types An and Dn. We show that the multiplication in the affine type De Concini–Kac–Procesi algebras arising from this smash product construction can be twisted by a cocycle to produce certain subalgebras related to the corresponding Faddeev–Reshetikhin–Takhtajan bialgebras.