Realisations of Quantum GL_p,q(2) and Jordanian GL_h,h'(2)

The quantum group GL_p,q(2) is known to be related to the Jordanian GL_h,h'(2) via a contraction procedure. It can also be realised using the generators of the Hopf algebra G_r,s. We contract the G_r,s quantum group to obtain its Jordanian analogue G_m,k, which provides a realisation of GL_h,h'(2) in a manner similar to the q-deformed case.Comment: 6 pages LaTex, Contribution to Proceedings of "8th International Colloquium on Quantum Groups and Integrable Systems", Prague, June 17 - 19, 199

The coloured quantum plane

We study the quantum plane associated to the coloured quantum group GL_{q}^{\lambda,\mu}(2) and solve the problem of constructing the corresponding differential geometric structure. This is achieved within the R-matrix framework generalising the Wess-Zumino formalism and leads to the concept of coloured quantum space. Both, the coloured Manin plane as well as the bicovariant differential calculus exhibit the colour exchange symmetry. The coloured h-plane corresponding to the coloured Jordanian quantum group GL_{h}^{\lambda,\mu}(2) is also obtained by contraction of the coloured q-plane.Comment: 10 pages, (AMS)LaTeX, to appear in J. Geom. Phy

Semientwining Structures and Their Applications

Semientwining structures are proposed as concepts simpler than entwining structures, yet they are shown to have interesting applications in constructing intertwining operators and braided algebras, lifting functors, finding solutions for Yang-Baxter systems, and so forth. While for entwining structures one can associate corings, for semientwining structures one can associate comodule algebra structures where the algebra involved is a bialgebra satisfying certain properties. Remove selecte

On the biparametric quantum deformation of GL(2) x GL(1)

We study the biparametric quantum deformation of GL(2) x GL(1) and exhibit its cross-product structure. We derive explictly the associated dual algebra, i.e., the quantised universal enveloping algebra employing the R-matrix procedure. This facilitates construction of a bicovariant differential calculus which is also shown to have a cross-product structure. Finally, a Jordanian analogue of the deformation is presented as a cross-product algebra.Comment: 16 pages LaTeX, published in JM