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

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

1999-11-24

arxiv.org/abs/math/9911194v1

J. Math. Phys. 41 (2000) 2403-2416

Mathematics

Quantum Algebra

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

Scientific paper

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{\lambda,\mu}(2) to yield a new Jordanian quantum group GL_m{\lambda,\mu}(2). Both G_r,s and G_m,k are then generalised to their coloured versions which inturn provide similar realisations of GL_r{\lambda,\mu}(2) and GL_m{\lambda,\mu}(2).

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