On \({\mathcal U}_ h(\text{sl}(2))\), \({\mathcal U}_ h(e(3))\) and their representations.

DOI10.1142/S0217751X97001341zbMATH Open1089.81502arXivq-alg/9610031MaRDI QIDQ2773884

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Publication date: 27 February 2002

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Abstract: By solving a set of recursion relations for the matrix elements of the ${calU}_h(sl(2))$ generators, the finite dimensional highest weight representations of the algebra were obtained as factor representations. Taking a nonlinear combination of the generators of the two copies of the ${calU}_h(sl(2))$ algebra, we obtained ${calU}_h(so(4))$ algebra. The latter, on contraction, yields ${calU}_h(e(3))$ algebra. A nonlinear map of ${calU}_h(e(3))$ algebra on its classical analogue $e(3)$ was obtained. The inverse mapping was found to be singular. It signifies a physically interesting situation, where in the momentum basis, a restricted domain of the eigenvalues of the classical operators is mapped on the whole real domain of the eigenvalues of the deformed operators.

Full work available at URL: https://arxiv.org/abs/q-alg/9610031

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