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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.

Sep 23, 2002
Sep 23, 2002
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