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 universalenveloping algebra U_q(g). The algebra U_q^w is a deformation of the universalenveloping algebra U(n_+\cap w.n_-). We construct smash products of certainfinite-type De Concini-Kac-Procesi algebras to obtain ones of affine type; wehave analogous constructions in types A_n and D_n. We show that themultiplication in the affine type De Concini-Kac-Procesi algebras arising fromthis smash product construction can be twisted by a cocycle to produce certainsubalgebras related to the corresponding Faddeev-Reshetikhin-Takhtajanbialgebras.
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