The FRT-Construction via Quantum Affine Algebras and Smash Products
Abstract
For every element w in the Weyl group of a simple Lie algebra g, De Concini, Kac, and Procesi defined a subalgebra Uqw of the quantized universal enveloping algebra Uq(g). The algebra Uqw 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.
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