Nonlinear deformed SU(2) algebras involving two deforming functions
Jun, 1996
8 pages
Published in:
- Czech.J.Phys. 46 (1996) 1189-1196
e-Print:
- q-alg/9701030 [math.QA]
DOI:
Report number:
- DEM-NT-96-07
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Abstract: (Springer)
The most common nonlinear deformations of the su(2) Lie algebra, introduced by Polychronakos and Roček, involve a single arbitrary function ofJo and include the quantum algebra suq(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 ofJo, 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 ofJo 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 byAq+(1), has two series of (N+1)-dimensional unitary irreducible representations, whereN=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.Note:
- 8 pages, LaTeX, no figures, submitted to Proc. 5th Int. Coll. ``Quantum Groups and Integrable Systems'', Prague, 20-22 June 1996 (to be published in Czech. J. Phys.)
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