%0 Journal Article
%T On ${\cal U}_h(sl(2))$, ${\cal U}_h(e(3))$ and their Representations
%A B. Abdesselam
%A A. Chakrabarti
%A R. Chakrabarti
%J Mathematics
%D 1996
%I arXiv
%R 10.1142/S0217751X97001341
%X By solving a set of recursion relations for the matrix elements of the ${\cal U}_h(sl(2))$ 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 ${\cal U}_h(sl(2))$ algebra, we obtained ${\cal U}_h(so(4))$ algebra. The latter, on contraction, yields ${\cal U}_h(e(3))$ algebra. A nonlinear map of ${\cal U}_h(e(3))$ 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.
%U http://arxiv.org/abs/q-alg/9610031v1