dorsal/arxiv
View SchemaOn ${\cal U}_h(sl(2))$, ${\cal U}_h(e(3))$ and their Representations
| Authors | B. Abdesselam, A. Chakrabarti, R. Chakrabarti |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9610031 |
| URL | https://arxiv.org/abs/q-alg/9610031 |
| DOI | 10.1142/S0217751X97001341 |
| Journal | Int. J. Mod. Phys. A, Vol. 12, No. 13 (1997) 2301-2319 |
Abstract
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.
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"abstract": "By solving a set of recursion relations for the matrix elements of the ${\\cal\nU}_h(sl(2))$ generators, the finite dimensional highest weight representations\nof the algebra were obtained as factor representations. Taking a nonlinear\ncombination of the generators of the two copies of the ${\\cal U}_h(sl(2))$\nalgebra, we obtained ${\\cal U}_h(so(4))$ algebra. The latter, on contraction,\nyields ${\\cal U}_h(e(3))$ algebra. A nonlinear map of ${\\cal U}_h(e(3))$\nalgebra on its classical analogue $e(3)$ was obtained. The inverse mapping was\nfound to be singular. It signifies a physically interesting situation, where in\nthe momentum basis, a restricted domain of the eigenvalues of the classical\noperators is mapped on the whole real domain of the eigenvalues of the deformed\noperators.",
"arxiv_id": "q-alg/9610031",
"authors": [
"B. Abdesselam",
"A. Chakrabarti",
"R. Chakrabarti"
],
"categories": [
"q-alg",
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],
"doi": "10.1142/S0217751X97001341",
"journal_ref": "Int. J. Mod. Phys. A, Vol. 12, No. 13 (1997) 2301-2319",
"title": "On ${\\cal U}_h(sl(2))$, ${\\cal U}_h(e(3))$ and their Representations",
"url": "https://arxiv.org/abs/q-alg/9610031"
},
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