The coloured quantum plane
arXiv:math/0202183 · doi:10.1016/S0393-0440(02)00051-7
Abstract
We study the quantum plane associated to the coloured quantum group GL_{q}^{λ,μ}(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}^{λ,μ}(2) is also obtained by contraction of the coloured q-plane.
10 pages, (AMS)LaTeX, to appear in J. Geom. Phys