ar X iv : q - a lg / 9 70 50 22 v 1 2 7 M ay 1 99 7 Coloured Hopf

ar X iv : q - a lg / 9 70 50 27 v 1 2 8 M ay 1 99 7 Jordanian U h , s gl ( 2 ) and its coloured realization

A two-parametric non-standard (Jordanian) deformation of the Lie algebra gl(2) is constructed, and then, exploited to obtain a new, triangular R-matrix solution of the coloured Yang-Baxter equation. The corresponding coloured quantum group is presented explicitly.

ar X iv : q - a lg / 9 70 50 20 v 1 2 7 M ay 1 99 7 QUANTUM GROUP DUALITY AND THE CUNTZ ALGEBRA

The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra Uq(g), and the structure of a co-module algebra over the quantum group Gq associated with Uq(g). These two algebraic structures are dual to each other via the duality between Gq and Uq(g).

ar X iv : q - a lg / 9 70 50 12 v 1 1 6 M ay 1 99 7 Poisson structures on the center

It is shown that the elliptic algebra Aq,p(ŝl(2)c) has a non trivial center at the critical level c = −2, generalizing the result of Reshetikhin and Semenov-Tian-Shansky for trigonometric algebras. A family of Poisson structures indexed by a non-negative integer k is constructed on this center.

ar X iv : q - a lg / 9 50 70 22 v 1 2 0 Ju l 1 99 5 QUANTUM PRINCIPAL BUNDLES AS HOPF - GALOIS EXTENSIONS

It is shown that every quantum principal bundle with a compact structure group is a Hopf-Galois extension. This property naturally extends to the level of general differential structures, so that every differential calculus over a quantum principal bundle with a compact structure group is a graded-differential variant of the Hopf-Galois extension.

ar X iv : q - a lg / 9 70 90 01 v 1 1 S ep 1 99 7 Bilinear identity for q - hypergeometric integrals