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MiS Preprint
88/2002
The coloured quantum plane
Deepak Parashar
Abstract
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.
