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 U_q^w of the quantized universal enveloping algebra U_q(g). The algebra U_q^w is a deformation of the universal enveloping algebra U(n_+\cap 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 A_n and D_n. 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.