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arxiv: math/0202183 · v1 · submitted 2002-02-18 · 🧮 math.QA · math-ph· math.MP

The coloured quantum plane

classification 🧮 math.QA math-phmath.MP
keywords colouredquantumplanecorrespondingdifferentialgrouplambdaachieved
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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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