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On Jordanian \(\text{U}_{h\alpha}\)(gl(2)) algebra and its \(T\) matrices via a contraction method. (English) Zbl 0934.17004

Summary: 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 colored 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 colored \(R_{q,\lambda}^{j_1,z_1;j_2,z_2}\) matrices of the standard \((q, l)\)-deformed U\(_{q,\lambda}\)(gl(2)) algebra. Moreover, by using the contraction process as a tool, the colored \(T_{h,\alpha}^{j,z}\) matrices for arbitrary \((j, z)\) representations of the Jordanian \(\text{Fun}_{h,\alpha}\)(GL(2)) algebra may be extracted from the corresponding \(T_{q,\lambda}^{j,z}\) matrices of the standard \(\text{Fun}_{q,\lambda}\)(GL(2)) algebra.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
16W35 Ring-theoretic aspects of quantum groups (MSC2000)

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