Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups

Abstract

The quantum group G_r,s provides a realisation of the two parameter quantum GL_p,q(2) which is known to be related to the two parameter nonstandard GL_hh'(2) group via a contraction method. We apply the contraction procedure to G_r,s and obtain a new Jordanian quantum group G_m,k. Furthermore, we provide a realisation of GL_h,h'(2) in terms of G_m,k. The contraction procedure is then extended to the coloured quantum group GL_r{λ,μ}(2) to yield a new Jordanian quantum group GL_m{λ,μ}(2). Both G_r,s and G_m,k are then generalised to their coloured versions which inturn provide similar realisations of GL_r{λ,μ}(2) and GL_m{λ,μ}(2).

22 pages LaTeX, to be published in J. Math. Phys

References in corpus (10)

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Cited by in corpus (3)

• The coloured quantum plane
• On the biparametric quantum deformation of GL(2) x GL(1)
• Coloured extension of GL_q(2) and its dual algebra