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

R. Chakrabarti; C. Quesne

doi:10.1142/S0217751X9900124X

paper

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

arXiv:math/9811064 · doi:10.1142/S0217751X9900124X

Abstract

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 ( $h, α$ ) Jordanian $R_{h, α}^{j_{1}, z_{1}; j_{2}, z_{2}}$ matrices of the U $_{h, α}$ (gl(2)) algebra may be derived from the corresponding coloured $R_{q, λ}^{j_{1}, z_{1}; j_{2}, z_{2}}$ matrices of the standard ( $q, λ$ )-deformed U $_{q, λ}$ (gl(2)) algebra. Moreover, by using the contraction process as a tool, the coloured $T_{h, α}^{j, z}$ matrices for arbitrary ( $j, z$ ) representations of the Jordanian Fun $_{h, α}$ (GL(2)) algebra may be extracted from the corresponding $T_{q, λ}^{j, z}$ matrices of the standard Fun $_{q, λ}$ (GL(2)) algebra.

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

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

Abstract

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