On Jordanian U_{h,α}(gl(2)) Algebra and Its T Matrices Via a Contraction Method

Details On Jordanian U_{h,α}(gl(2)) Algebra and Its T Matrices Via a Contraction Method On Jordanian U_{h,α}(gl(2)) Algebra and Its T Matrices Via a Contraction Method

1998-11-10

arxiv.org/abs/math/9811064v1

Int. J. Mod. Phys. A 14 (1999) 2511-2529

Mathematics

Quantum Algebra

LaTeX, uses amssym.sty, 24 pages, no figure, to be published in Int. J. Mod. Phys. A

Scientific paper

10.1142/S0217751X9900124X

The $R_h^{j_1;j_2}$ matrices of the Jordanian U$_h$(sl(2)) algebra at arbitrary dimensions may be obtained from the corresponding $R_q^{j_1;j_2}$ matrices of the standard $q$-deformed U$_q$(sl(2)) algebra through a contraction technique. By extending this method, the coloured two-parametric ($h, \alpha$) Jordanian $R_{h,\alpha}^{j_1,z_1;j_2,z_2}$ matrices of the U$_{h,\alpha}$(gl(2)) algebra may be derived from the corresponding coloured $R_{q,\lambda}^{j_1,z_1;j_2,z_2}$ matrices of the standard ($q, \lambda$)-deformed U$_{q,\lambda}$(gl(2)) algebra. Moreover, by using the contraction process as a tool, the coloured $T_{h,\alpha}^{j,z}$ matrices for arbitrary ($j, z$) representations of the Jordanian Fun$_{h,\alpha}$(GL(2)) algebra may be extracted from the corresponding $T_{q,\lambda}^{j,z}$ matrices of the standard Fun$_{q,\lambda}$(GL(2)) algebra.

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