The coloured quantum plane

Details The coloured quantum plane The coloured quantum plane

2002-02-18

arxiv.org/abs/math/0202183v1

J. Geom. Phys. 44 (2003) 481-488

Mathematics

Quantum Algebra

10 pages, (AMS)LaTeX, to appear in J. Geom. Phys

Scientific paper

10.1016/S0393-0440(02)00051-7

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.

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