MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

The coloured quantum plane

Deepak Parashar


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.

MSC Codes:
81R50, 17B37
quantum groups, manin plane, differential calculus

Related publications

2003 Repository Open Access
Deepak Parashar

The coloured quantum plane

In: Journal of geometry and physics, 44 (2003) 4, pp. 481-488