MiS Preprint Repository

We study the quantum plane associated to the coloured quantum group $G{L}_q^{\lambda ,\mu }(2)$ 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 $G{L}_h^{\lambda ,\mu }(2)$ is also obtained by contraction of the coloured $q$-plane.