English

The coloured quantum plane

Quantum Algebra 2009-11-07 v1 Mathematical Physics math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.math/0202183,
  title  = {The coloured quantum plane},
  author = {Deepak Parashar},
  journal= {arXiv preprint arXiv:math/0202183},
  year   = {2009}
}

Comments

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