On nonlinear angular momentum theories, their representations and associated Hopf structures

@article{Abdesselam1996OnNA,
  title={On nonlinear angular momentum theories, their representations and associated Hopf structures},
  author={Boucif Abdesselam and Jules Beckers and Amitabha Chakrabarti and N.Debergh},
  journal={Journal of Physics A},
  year={1996},
  volume={29},
  pages={3075-3088}
}
Nonlinear sl(2) algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases. We construct their unitary irreducible representations in such a general context. The linear sl(2) case as well as its q-deformation are easily recovered as specific examples. Two other physically interesting applications corresponding to the so-called Higgs and quadratic algebras are also considered. We show that these two nonlinear algebras can be equipped with a… 
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References

SHOWING 1-10 OF 41 REFERENCES
GENERALIZED DEFORMED su(2) ALGEBRAS, DEFORMED PARAFERMIONIC OSCILLATORS AND FINITE W-ALGEBRAS
Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a two-dimensional curved space) and mathematical structures (quadratic algebra QH(3),
Generalized deformed algebras F(A1) and their applications
  • F. Pan
  • Mathematics, Physics
  • 1994
Generalized deformation of A1 is proposed. Some generalized deformed algebras F(A1) and their unitary representations are discussed in detail. F(A1) involves not only Lie algebras SU(2), SU(1,1), E2
The 'Higgs algebra' as a 'quantum' deformation of SU(2)
The Higgs algebra (i.e., the hidden symmetry algebra of the Coulomb problem in the two-dimensional space of constant curvature) is investigated. Consisting of 3 generators, the Higgs algebra can be
Aq-difference analogue of U(g) and the Yang-Baxter equation
Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced. Its structure and representations are studied in the simplest case g=sl(2). It is then applied
Dynamical symmetries in a spherical geometry. I
The two potentials for which a particle moving non-relativistically in a spherical space under the action of conservative central force executes closed orbits are found. When the curvature is zero
Quantum Groups
Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups
Deformed oscillator algebras for two-dimensional quantum superintegrable systems.
TLDR
The method shows how quantum algebraic techniques can simplify the study of quantum superintegrable systems, especially in two dimensions.
...
1
2
3
4
5
...