Preprint 88/2002

The coloured quantum plane

Deepak Parashar

Contact the author: Please use for correspondence this email.
Submission date: 23. Sep. 2002
Pages: 12
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
Download full preprint: PDF (156 kB), PS ziped (177 kB)

We study the quantum plane associated to the coloured quantum group formula7 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 formula13 is also obtained by contraction of the coloured q-plane.

18.07.2014, 01:41