dorsal/arxiv
View SchemaNonlinear deformed su(2) algebras involving two deforming functions
| Authors | D. Bonatsos, C. Daskaloyannis, P. Kolokotronis, A. Ludu, C. Quesne |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9701030 |
| URL | https://arxiv.org/abs/q-alg/9701030 |
| DOI | 10.1007/BF01690332 |
| Journal | Czech. J. Phys. 46 (1996) 1189-1196 |
Abstract
The most common nonlinear deformations of the su(2) Lie algebra, introduced by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and include the quantum algebra su_q(2) as a special case. In the present contribution, less common nonlinear deformations of su(2), introduced by Delbecq and Quesne and involving two deforming functions of J_0, are reviewed. Such algebras include Witten's quadratic deformation of su(2) as a special case. Contrary to the former deformations, for which the spectrum of J_0 is linear as for su(2), the latter give rise to exponential spectra, a property that has aroused much interest in connection with some physical problems. Another interesting algebra of this type, denoted by ${\cal A}^+_q(1)$, has two series of (N+1)-dimensional unitary irreducible representations, where N=0, 1, 2, .... To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed. The resulting algebraic structure, referred to as a two-colour quasitriangular Hopf algebra, is described.
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"abstract": "The most common nonlinear deformations of the su(2) Lie algebra, introduced\nby Polychronakos and Ro\\v cek, involve a single arbitrary function of J_0 and\ninclude the quantum algebra su_q(2) as a special case. In the present\ncontribution, less common nonlinear deformations of su(2), introduced by\nDelbecq and Quesne and involving two deforming functions of J_0, are reviewed.\nSuch algebras include Witten\u0027s quadratic deformation of su(2) as a special\ncase. Contrary to the former deformations, for which the spectrum of J_0 is\nlinear as for su(2), the latter give rise to exponential spectra, a property\nthat has aroused much interest in connection with some physical problems.\nAnother interesting algebra of this type, denoted by ${\\cal A}^+_q(1)$, has two\nseries of (N+1)-dimensional unitary irreducible representations, where N=0, 1,\n2, .... To allow the coupling of any two such representations, a generalization\nof the standard Hopf axioms is proposed. The resulting algebraic structure,\nreferred to as a two-colour quasitriangular Hopf algebra, is described.",
"arxiv_id": "q-alg/9701030",
"authors": [
"D. Bonatsos",
"C. Daskaloyannis",
"P. Kolokotronis",
"A. Ludu",
"C. Quesne"
],
"categories": [
"q-alg",
"hep-th",
"math-ph",
"math.MP",
"math.QA"
],
"doi": "10.1007/BF01690332",
"journal_ref": "Czech. J. Phys. 46 (1996) 1189-1196",
"title": "Nonlinear deformed su(2) algebras involving two deforming functions",
"url": "https://arxiv.org/abs/q-alg/9701030"
},
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