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

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.