par Quesne, Christiane
Référence Journal of mathematical physics, 39, 2, page (1199-1222)
Publication Publié, 1998-02
Article révisé par les pairs
Résumé : We extend the notion of dually conjugate Hopf (super)algebras to the colored Hopf (super)algebras ℋc that we recently introduced. We show that if the standard Hopf (super)algebras ℋq that are the building blocks of ℋc have Hopf duals ℋ*q, then the latter may be used to construct coloured Hopf duals ℋc*, endowed with colored algebra and antipode maps, but with a standard coalgebraic structure. Next, we review the case where the ℋq's are quantum universal enveloping algebras of Lie (super)algebras Uq(g), so that the corresponding ℋ*q's are quantum (super) groups Gq. We extend the Fronsdal and Galindo universal script T sign-matrix formalism to the colored pairs (Uc(g),Gc) by defining colored universal script T sign-matrices. We then show that together with the colored universal ℛ-matrices previously introduced, the latter provide an algebraic formulation of the colored RTT-relations, proposed by Basu-Mallick. This establishes a link between the colored extensions of Drinfeld-Jimbo and Faddeev-Reshetikhin-Takhtajan pictures of quantum groups and quantum algebras. Finally, we illustrate the construction of colored pairs by giving some explicit results for the two-parameter deformations of (U(gl(2)),Gl(2)), and (U(gl(1/1)),Gl(1/1)). © 1998 American Institute of Physics.