The coloured quantum plane
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Submission date: 23. Sep. 2002
published in: Journal of geometry and physics, 44 (2003) 4, p. 481-488
DOI number (of the published article): 10.1016/S0393-0440(02)00051-7
MSC-Numbers: 81R50, 17B37
Keywords and phrases: quantum groups, manin plane, differential calculus
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We study the quantum plane associated to the coloured quantum group 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 is also obtained by contraction of the coloured q-plane.